| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
y^{\prime }&=y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.175 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.347 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.142 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x} \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.977 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.059 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.896 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.611 |
|
| \begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.530 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.931 |
|
| \begin{align*}
x y^{\prime }+5 y&=7 x^{2} \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.884 |
|
| \begin{align*}
2 x y^{\prime }+y&=10 \sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.496 |
|
| \begin{align*}
3 x y^{\prime }+y&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
x y^{\prime }-y&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.415 |
|
| \begin{align*}
2 x y^{\prime }-3 y&=9 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.561 |
|
| \begin{align*}
x y^{\prime }+y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| \begin{align*}
x y^{\prime }+3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.034 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.785 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.812 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| \begin{align*}
x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.684 |
|
| \begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.528 |
|
| \begin{align*}
x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.740 |
|
| \begin{align*}
\frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.469 |
|
| \begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.104 |
|
| \begin{align*}
\frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| \begin{align*}
y^{\prime }&=1+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \begin{align*}
2 x y^{\prime }&=y+2 x \cos \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.721 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.700 |
|
| \begin{align*}
x^{3}+3 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
3 y+x^{4} y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.248 |
|
| \begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.828 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.982 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| \begin{align*}
x y^{\prime }+y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.967 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.539 |
|
| \begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.554 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.600 |
|
| \begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.803 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
y^{\prime }&=y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.861 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.770 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x} \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.437 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.181 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.671 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.388 |
|
| \begin{align*}
2 x y^{\prime }+y&=10 \sqrt {x} \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.304 |
|
| \begin{align*}
2 x y^{\prime }+y&=10 \sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.657 |
|
| \begin{align*}
3 x y^{\prime }+y&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
x y^{\prime }-y&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.860 |
|
| \begin{align*}
2 x y^{\prime }-3 y&=9 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.707 |
|
| \begin{align*}
x y^{\prime }+y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.776 |
|
| \begin{align*}
x y^{\prime }+3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.762 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.718 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.451 |
|
| \begin{align*}
x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.976 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.529 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.108 |
|
| \begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.944 |
|
| \begin{align*}
x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.151 |
|
| \begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.339 |
|
| \begin{align*}
x^{3}+3 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
3 y+x^{4} y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.756 |
|
| \begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| \begin{align*}
x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.826 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.177 |
|
| \begin{align*}
x y^{\prime }+y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.435 |
|
| \begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.433 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| \begin{align*}
3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.605 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| \begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.078 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.274 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.496 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.307 |
|
| \begin{align*}
2 y t +y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.812 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
-y+t y^{\prime }&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| \begin{align*}
y+y^{\prime }&=5 \sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.269 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.160 |
|
| \begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.088 |
|
| \begin{align*}
2 y+t y^{\prime }&=t^{2}-t +1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.773 |
|
| \begin{align*}
\frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.576 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| \begin{align*}
4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=t \\
y \left (\ln \left (2\right )\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
-y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.764 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
2 y+t y^{\prime }&=\frac {\sin \left (t \right )}{t} \\
y \left (-\frac {\pi }{2}\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| \begin{align*}
\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
29.522 |
|
| \begin{align*}
\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| \begin{align*}
\frac {2 y}{3}+y^{\prime }&=1-\frac {t}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.146 |
|
| \begin{align*}
\frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
-y+y^{\prime }&=1+3 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| \begin{align*}
-\frac {3 y}{2}+y^{\prime }&=2 \,{\mathrm e}^{t}+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.424 |
|
| \begin{align*}
\ln \left (t \right ) y+\left (-3+t \right ) y^{\prime }&=2 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.240 |
|
| \begin{align*}
y+\left (-4+t \right ) t y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.774 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| \begin{align*}
y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.355 |
|
| \begin{align*}
\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.302 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.205 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}-2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| \begin{align*}
y^{\prime }&=3-6 x +y-2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
y x +x y^{\prime }&=1-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| \begin{align*}
x y^{\prime }+2 y&=\frac {\sin \left (x \right )}{x} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{1+{\mathrm e}^{x}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y^{\prime }&=y-y \,{\mathrm e}^{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.056 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+3 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.920 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&={\mathrm e}^{2 t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.967 |
|
| \begin{align*}
3 t +2 y&=-t y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.321 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.424 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-y \tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi \sqrt {2}}{8} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.704 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-2 x^{2} y+2}{x^{3}} \\
y \left (1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.196 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.453 |
|
| \begin{align*}
x y^{\prime }+3 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.420 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.440 |
|
| \begin{align*}
x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.272 |
|
| \begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
y^{\prime }+\frac {k y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| \begin{align*}
y^{\prime }+\tan \left (k x \right ) y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.428 |
|
| \begin{align*}
y^{\prime }+\left (\frac {1}{x}-1\right ) y&=-\frac {2}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {{\mathrm e}^{-x^{2}}}{x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.926 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x -1}&=\frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| \begin{align*}
x y^{\prime }+\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.067 |
|
| \begin{align*}
x y^{\prime }+2 y&=\frac {2}{x^{2}}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {\sin \left (x \right )}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.099 |
|
| \begin{align*}
\left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y&=\left (x -2\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \begin{align*}
y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
x^{2} y^{\prime }+3 y x&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.031 |
|
| \begin{align*}
y^{\prime }+7 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
x y^{\prime }+3 y&=\frac {2}{x \left (x^{2}+1\right )} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {2}{x^{2}}+1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+3 y&=\frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.652 |
|
| \begin{align*}
x y^{\prime }+2 y&=8 x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.669 |
|
| \begin{align*}
x y^{\prime }-2 y&=-x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.583 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.865 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }+4 y&=\frac {2 x^{2}+1}{x \left (x +2\right )^{3}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 y x&=x \left (x^{2}-1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
x y^{\prime }-2 y&=-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.168 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.542 |
|
| \begin{align*}
y^{\prime }+2 x \left (y+1\right )&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.598 |
|
| \begin{align*}
\left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| \begin{align*}
3 \cos \left (x \right ) y+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
61.855 |
|
| \begin{align*}
\sin \left (x \right )-y \sin \left (x \right )-2 \cos \left (x \right )+\cos \left (x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.402 |
|
| \begin{align*}
\left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.692 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
3 x^{2} y+2 x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.676 |
|
| \begin{align*}
5 y x +2 y+5+2 x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.706 |
|
| \begin{align*}
y x +x +2 y+1+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.166 |
|
| \begin{align*}
x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.662 |
|
| \begin{align*}
-y+\left (x^{4}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
y^{\prime }+\sin \left (t \right ) y&=0 \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime }-2 y t&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
2 y t +y^{\prime }&=t \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.841 |
|
| \begin{align*}
\frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.856 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.959 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.937 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| \begin{align*}
\frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.999 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\
y \left (0\right ) &= \sqrt {5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
y^{\prime }-2 y t&=t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.949 |
|
| \begin{align*}
y t +y^{\prime }&=t +1 \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.175 |
|
| \begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| \begin{align*}
y^{\prime }-2 y t&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
y t +\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.067 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=\frac {1}{t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {t}}&={\mathrm e}^{\frac {\sqrt {t}}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.278 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=\cos \left (t \right )+\frac {\sin \left (t \right )}{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.203 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.233 |
|
| \begin{align*}
3 t y^{\prime }&=\cos \left (t \right ) y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.849 |
|
| \begin{align*}
y^{\prime }&=t \left (1+y\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.654 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.914 |
|
| \begin{align*}
\frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.932 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| \begin{align*}
\frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.856 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\
y \left (0\right ) &= \sqrt {5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.567 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.796 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.847 |
|
| \begin{align*}
y^{\prime }-2 y t&=t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.128 |
|
| \begin{align*}
y t +y^{\prime }&=t +1 \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.528 |
|
| \begin{align*}
y^{\prime }-2 y t&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.966 |
|
| \begin{align*}
y t +\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.907 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\
y \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.133 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.459 |
|
| \begin{align*}
3 t y^{\prime }&=\cos \left (t \right ) y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.371 |
|
| \begin{align*}
y^{\prime }&=2 t \left (1+y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.199 |
|
| \begin{align*}
y^{\prime }&=t \left (1+y\right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.949 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.102 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.181 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-1+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.547 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }-y&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.717 |
|
| \begin{align*}
y+3+\cot \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.315 |
|
| \begin{align*}
y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.833 |
|
| \begin{align*}
y&=y x +x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.650 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \begin{align*}
x y^{\prime }+2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.245 |
|
| \begin{align*}
x +y&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.143 |
|
| \begin{align*}
y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| \begin{align*}
\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.102 |
|
| \begin{align*}
x y^{\prime }+\ln \left (x \right )-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.822 |
|
| \begin{align*}
\left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.387 |
|
| \begin{align*}
x y^{\prime }+2 y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.799 |
|
| \begin{align*}
y^{\prime }-y x&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.258 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.711 |
|
| \begin{align*}
y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.581 |
|
| \begin{align*}
x^{\prime }+x&={\mathrm e}^{-y} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.179 |
|
| \begin{align*}
y x^{\prime }+\left (y +1\right ) x&={\mathrm e}^{y} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
x y^{\prime }-2 x^{4}-2 y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.355 |
|
| \begin{align*}
y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
x y^{\prime }&=5 y+x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.484 |
|
| \begin{align*}
x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
\cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right )&=\cos \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.671 |
|
| \begin{align*}
y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.794 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )-\sec \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.644 |
|
| \begin{align*}
2 y-y x -3+x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y&=0 \\
y \left (0\right ) &= -6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }-y-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.150 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.608 |
|
| \begin{align*}
r^{\prime }&=r \cot \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
y^{\prime }+x +y \cot \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| \begin{align*}
x y^{\prime }&=x^{4}+4 y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| \begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| \begin{align*}
2 y x -2 y+1+x \left (x -1\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.212 |
|
| \begin{align*}
y^{\prime }+P \left (x \right ) y&=Q \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.271 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.871 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime }&=\left (t^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.330 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{-3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \begin{align*}
y^{\prime }&=t -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| \begin{align*}
t y^{\prime }&=y+t^{3} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.604 |
|
| \begin{align*}
y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.664 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t +1} \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.477 |
|
| \begin{align*}
t y^{\prime }&=-y+t^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.561 |
|
| \begin{align*}
y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \\
y \left (\frac {\pi }{8}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.671 |
|
| \begin{align*}
t \ln \left (t \right ) y^{\prime }&=t \ln \left (t \right )-y \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.397 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.349 |
|
| \begin{align*}
y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.298 |
|
| \begin{align*}
\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.672 |
|
| \begin{align*}
2 x y^{\prime }+3 x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.503 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
8.500 |
|
| \begin{align*}
y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.941 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.081 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.883 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=1 \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.403 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.332 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.940 |
|
| \begin{align*}
y-\left (x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.958 |
|
| \begin{align*}
-x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.459 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.825 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.014 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.165 |
|
| \begin{align*}
2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.777 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \begin{align*}
x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.872 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \begin{align*}
y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
y-\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.202 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
-x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.858 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.882 |
|
| \begin{align*}
y^{\prime }+y&=4 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.234 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.203 |
|
| \begin{align*}
x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.256 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| \begin{align*}
1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.225 |
|
| \begin{align*}
y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
y^{\prime }+\frac {m y}{x}&=\ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=4 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.100 |
|
| \begin{align*}
x^{\prime }+\frac {2 x}{4-t}&=5 \\
x \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.770 |
|
| \begin{align*}
y-{\mathrm e}^{x}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| \begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.763 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.803 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.425 |
|
| \begin{align*}
3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.316 |
|
| \begin{align*}
y^{\prime }&=\frac {y-2 x}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
y^{\prime }+y&=x^{2}+2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| \begin{align*}
x y^{\prime }&=x +y \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.945 |
|
| \begin{align*}
y^{\prime }-3 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \\
y \left (5\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.981 |
|
| \begin{align*}
x y^{\prime }+2 y&=\left (3 x +2\right ) {\mathrm e}^{3 x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.099 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.135 |
|
| \begin{align*}
y^{\prime }-y&=x^{3} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.484 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.386 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.380 |
|
| \begin{align*}
y^{\prime }+y \ln \left (x \right )&=x^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
x y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.877 |
|
| \begin{align*}
x y^{\prime }-y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.636 |
|
| \begin{align*}
x y^{\prime }+n y&=x^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| \begin{align*}
x y^{\prime }-n y&=x^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.302 |
|
| \begin{align*}
\left (x^{3}+x \right ) y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.611 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.498 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.128 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y-\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.441 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.174 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.719 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.233 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.615 |
|
| \begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }+y&=2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.701 |
|
| \begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }-y&=2 \sqrt {x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.480 |
|
| \begin{align*}
\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.672 |
|
| \begin{align*}
\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y&=\sqrt {x +a}-\sqrt {x +b} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.401 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.702 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x y}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.892 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x^{2}-1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.978 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.964 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.963 |
|
| \begin{align*}
x y^{\prime }&=y x +y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.344 |
|
| \begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.712 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.270 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.585 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.964 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.368 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.499 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.274 |
|
| \begin{align*}
2 y-x^{3}&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \begin{align*}
x y^{\prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.610 |
|
| \begin{align*}
x^{2}+y&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.612 |
|
| \begin{align*}
\ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.810 |
|
| \begin{align*}
1+\cos \left (x \right ) y-\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
\left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y^{\prime }&=1+3 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
\left (1+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
y^{\prime }&=\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-y&=x \left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| \begin{align*}
y-1-y x +x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| \begin{align*}
y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| \begin{align*}
y \sin \left (x \right )+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.245 |
|
| \begin{align*}
\left (1+\cos \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.597 |
|
| \begin{align*}
y^{\prime }&=x +\sin \left (x \right )+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.969 |
|
| \begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.929 |
|
| \begin{align*}
y^{\prime }&=a +b x +c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| \begin{align*}
y^{\prime }&=a \cos \left (b x +c \right )+k y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.861 |
|
| \begin{align*}
y^{\prime }&=a \sin \left (b x +c \right )+k y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.697 |
|
| \begin{align*}
y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.723 |
|
| \begin{align*}
y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.580 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.345 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )+\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.112 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )-\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.085 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.966 |
|
| \begin{align*}
y^{\prime }&=y \cot \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.397 |
|
| \begin{align*}
y^{\prime }&=1-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
y^{\prime }&=x \csc \left (x \right )-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.970 |
|
| \begin{align*}
y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.616 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.042 |
|
| \begin{align*}
y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.948 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.335 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.905 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| \begin{align*}
y^{\prime }&=y \tan \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )-y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )-y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.278 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )+2 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.211 |
|
| \begin{align*}
y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.877 |
|
| \begin{align*}
y^{\prime }&=\csc \left (x \right )+3 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.093 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right )+\left (-1+\sin \left (x \right )\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.457 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.625 |
|
| \begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.071 |
|
| \begin{align*}
x y^{\prime }&=x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.066 |
|
| \begin{align*}
x y^{\prime }&=1+x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
x y^{\prime }&=x^{m}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.307 |
|
| \begin{align*}
x y^{\prime }&=x \sin \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.692 |
|
| \begin{align*}
x y^{\prime }&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| \begin{align*}
x y^{\prime }&=x^{n} \ln \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.857 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x \right )-2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| \begin{align*}
x y^{\prime }&=a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.353 |
|
| \begin{align*}
x y^{\prime }&=-a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.484 |
|
| \begin{align*}
x y^{\prime }&=1+x +a y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.378 |
|
| \begin{align*}
x y^{\prime }&=a x +b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.083 |
|
| \begin{align*}
x y^{\prime }&=a +b \,x^{n}+c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.365 |
|
| \begin{align*}
x y^{\prime }+2+\left (-x +3\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.764 |
|
| \begin{align*}
x y^{\prime }+x +\left (a x +2\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.711 |
|
| \begin{align*}
x y^{\prime }+\left (b x +a \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.244 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.111 |
|
| \begin{align*}
x y^{\prime }&=a x -\left (-b \,x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.031 |
|
| \begin{align*}
x y^{\prime }+\left (-a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.134 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.148 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&={\mathrm e}^{x} \left (x +1\right )^{n +1}+n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.739 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=2 \left (x +a \right )^{5}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.102 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b +c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.614 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=-b -c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.001 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.030 |
|
| \begin{align*}
2 x y^{\prime }&=2 x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
28.911 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.914 |
|
| \begin{align*}
2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| \begin{align*}
x^{2} y^{\prime }&=a -y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.096 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.829 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.773 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.441 |
|
| \begin{align*}
x^{2} y^{\prime }+x \left (x +2\right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.156 |
|
| \begin{align*}
x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.261 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.629 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+1&=y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.467 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-1&=y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.046 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a +y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.375 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.242 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.062 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.478 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.526 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.639 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3 x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.553 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.324 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x -y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.744 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right )&=2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.691 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.109 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=a +4 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.417 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.738 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.839 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +\left (x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.486 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=2 y x +2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=2 y x -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.414 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.038 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +2 \left (2-x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.631 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.573 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.299 |
|
| \begin{align*}
\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.830 |
|
| \begin{align*}
\left (x +a \right )^{2} y^{\prime }&=2 \left (x +a \right ) \left (b +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.116 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.625 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=\left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.452 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.941 |
|
| \begin{align*}
2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.775 |
|
| \begin{align*}
2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.462 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \begin{align*}
2 \left (x^{2}+x +1\right ) y^{\prime }&=1+8 x^{2}-\left (2 x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
20.510 |
|
| \begin{align*}
4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| \begin{align*}
x \left (a x +1\right ) y^{\prime }+a -y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.544 |
|
| \begin{align*}
x^{3} y^{\prime }&=b \,x^{2} y+a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| \begin{align*}
x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.126 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.501 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.695 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.504 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.276 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.595 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.659 |
|
| \begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \begin{align*}
x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.292 |
|
| \begin{align*}
x^{5} y^{\prime }&=1-3 x^{4} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.532 |
|
| \begin{align*}
x^{n} y^{\prime }&=a +b \,x^{n -1} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.616 |
|
| \begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }&=2 x -y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.383 |
|
| \begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+x +y&=\sqrt {a^{2}+x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.037 |
|
| \begin{align*}
\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime }&=\tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.209 |
|
| \begin{align*}
\left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| \begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.751 |
|
| \begin{align*}
\left (a_{0} +a_{1} \sin \left (x \right )^{2}\right ) y^{\prime }+a_{2} x \left (a_{3} +a_{1} \sin \left (x \right )^{2}\right )+a_{1} y \sin \left (2 x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
14.157 |
|
| \begin{align*}
\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }&=a x \left (1+\ln \left (x \right )\right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| \begin{align*}
1-y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.249 |
|
| \begin{align*}
\left (x +a \right ) \left (x +b \right ) y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.252 |
|
| \begin{align*}
y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.051 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.763 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.973 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.502 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
33.221 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.433 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.619 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{y^{\prime }+y^{2}}&=\frac {-x y^{\prime }+y}{1+x^{2} y^{\prime }} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.202 |
|
| \begin{align*}
7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.941 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.448 |
|
| \begin{align*}
x^{\prime }+2 x y&={\mathrm e}^{-y^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.754 |
|
| \begin{align*}
r^{\prime }&=\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.796 |
|
| \begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.516 |
|
| \begin{align*}
\tan \left (\theta \right ) r^{\prime }-r&=\tan \left (\theta \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.174 |
|
| \begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.422 |
|
| \begin{align*}
2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.063 |
|
| \begin{align*}
2 y+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.774 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.326 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
x y^{\prime }+y&=x \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.415 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.387 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.576 |
|
| \begin{align*}
2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \begin{align*}
y^{\prime }+a y&=k \,{\mathrm e}^{b x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
y^{\prime }+a y&=b \sin \left (k x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.115 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| \begin{align*}
x y^{\prime }+a y+b \,x^{n}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.378 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.935 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{a x}+a y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.299 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.274 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
x^{2} y^{\prime }+3 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
2 x y^{\prime }+y&=2 x^{{5}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}&=\frac {1}{x +\sqrt {x^{2}+1}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.247 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y^{\prime }+2 y \,{\mathrm e}^{x}&=\left (1+{\mathrm e}^{x}\right ) {\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +2 x \sqrt {-x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
x^{\prime }&=\cos \left (y \right )-x \tan \left (y \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x^{\prime }+x-{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.282 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=\frac {1}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \begin{align*}
y+2 x -x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.733 |
|
| \begin{align*}
\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2}&=r \cos \left (\theta \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.296 |
|
| \begin{align*}
3 x^{2} y+x^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.151 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \\
y \left (2\right ) &= 6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| \begin{align*}
x y^{\prime }&=y x +y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.523 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| \begin{align*}
x^{\prime }&=3 x t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.125 |
|
| \begin{align*}
y^{\prime }&=x^{3} \left (1-y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (y+1\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.095 |
|
| \begin{align*}
y^{\prime }&=2 y-2 y t \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| \begin{align*}
x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.196 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=y t -y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| \begin{align*}
3 t&={\mathrm e}^{t} y^{\prime }+\ln \left (t \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.681 |
|
| \begin{align*}
3 r&=r^{\prime }-\theta ^{3} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.446 |
|
| \begin{align*}
y^{\prime }-y-{\mathrm e}^{3 x}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.574 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+2 x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
r^{\prime }+r \tan \left (\theta \right )&=\sec \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.148 |
|
| \begin{align*}
x y^{\prime }+2 y&=\frac {1}{x^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
t +y+1-y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| \begin{align*}
y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| \begin{align*}
y x^{\prime }+2 x&=5 y^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
x y^{\prime }+3 x^{2}+3 y&=\frac {\sin \left (x \right )}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x^{2} y&=\left (x +1\right ) \sqrt {-x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.739 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= {\mathrm e}-1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
y^{\prime }+4 y-{\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= {\frac {4}{3}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \begin{align*}
t^{2} x^{\prime }+3 x t&=t^{4} \ln \left (t \right )+1 \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}+2&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=2 x \cos \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.072 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.174 |
|
| \begin{align*}
y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.136 |
|
| \begin{align*}
x^{\prime }&=\alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.485 |
|
| \begin{align*}
x^{{10}/{3}}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.542 |
|
| \begin{align*}
{\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.900 |
|
| \begin{align*}
{\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0 \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.216 |
|
| \begin{align*}
x^{2} \sin \left (x \right )+4 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
x^{4}-x +y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{\prime }-4 y&=32 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.193 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\sin \left (2 x \right ) x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )+\sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.838 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| \begin{align*}
t +x+3+x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.310 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}+1}-y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \begin{align*}
y^{\prime }+a y&=Q \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x -x +1&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| \begin{align*}
y^{\prime }+y&=\left (x +1\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=\sinh \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| \begin{align*}
y^{\prime }+\frac {y}{1-x}+2 x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.473 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}-x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.768 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}-x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.594 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.820 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.904 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.067 |
|
| \begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.294 |
|
| \begin{align*}
x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.030 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| \begin{align*}
x y^{\prime }-y&=x^{3}+3 x^{2}-2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
x y^{\prime }-y&=x^{3} \cos \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=5 \,{\mathrm e}^{\cos \left (x \right )} \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| \begin{align*}
y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.965 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.405 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (y+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.526 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x -1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.101 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| \begin{align*}
y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.209 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.964 |
|
| \begin{align*}
y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.042 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.718 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.875 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.402 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| \begin{align*}
4 y+x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.162 |
|
| \begin{align*}
1+2 y+\left (-x^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.070 |
|
| \begin{align*}
1+y-\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.024 |
|
| \begin{align*}
1+2 y-\left (4-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.711 |
|
| \begin{align*}
x y^{\prime }+2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \begin{align*}
y^{\prime }+y&=2 x +2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \begin{align*}
y^{\prime }-y&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| \begin{align*}
-3 y-\left (x -2\right ) {\mathrm e}^{x}+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.302 |
|
| \begin{align*}
i^{\prime }-6 i&=10 \sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
x y^{\prime }&=y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.918 |
|
| \begin{align*}
x y^{\prime }&=2 y+{\mathrm e}^{x} x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.133 |
|
| \begin{align*}
L i^{\prime }+R i&=E \sin \left (2 t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \begin{align*}
x y^{\prime }&=1-x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.699 |
|
| \begin{align*}
y^{\prime }+y x&=\frac {1}{x^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.948 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
x y^{\prime }-3 y x&=1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| \begin{align*}
2 x y^{\prime }-y&=2 x \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.415 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.456 |
|
| \begin{align*}
y^{\prime }+2 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \begin{align*}
x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.468 |
|
| \begin{align*}
3 x y^{\prime }+5 y&=10 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.459 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.971 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.210 |
|
| \begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.107 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.647 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.035 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.022 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.918 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.915 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.840 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.626 |
|
| \begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.097 |
|
| \begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.843 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.636 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.086 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.645 |
|
| \begin{align*}
y^{\prime }&=x^{2}-2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
x y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.218 |
|
| \begin{align*}
n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.948 |
|
| \begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.886 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\
y \left (4\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.635 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.049 |
|
| \begin{align*}
y^{\prime }+2 y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.112 |
|
| \begin{align*}
y^{\prime }&=2 y+x^{2}+5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.159 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.794 |
|
| \begin{align*}
4 y+x y^{\prime }&=x^{3}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.867 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-y x&=x^{2}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.435 |
|
| \begin{align*}
x^{2} y^{\prime }+x \left (x +2\right ) y&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| \begin{align*}
\cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.603 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.968 |
|
| \begin{align*}
\left (x +2\right )^{2} y^{\prime }&=5-8 y-4 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
r^{\prime }+r \sec \left (t \right )&=\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.117 |
|
| \begin{align*}
p^{\prime }+2 t p&=p+4 t -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| \begin{align*}
x y^{\prime }+\left (1+3 x \right ) y&={\mathrm e}^{-3 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.406 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y&=\left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| \begin{align*}
y^{\prime }&=x +5 y \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.627 |
|
| \begin{align*}
y^{\prime }&=2 x -3 y \\
y \left (0\right ) &= {\frac {1}{3}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \begin{align*}
x y^{\prime }+y&={\mathrm e}^{x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.690 |
|
| \begin{align*}
x y^{\prime }+y&=1+4 x \\
y \left (1\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.649 |
|
| \begin{align*}
y^{\prime }+4 y x&=x^{3} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }+y x&=1 \\
y \left ({\mathrm e}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=2 \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\cos \left (x \right )^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.604 |
|
| \begin{align*}
2 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.135 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.366 |
|
| \begin{align*}
y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.713 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.888 |
|
| \begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y&=4 x \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.186 |
|
| \begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.112 |
|
| \begin{align*}
y^{\prime }-2 y x&=1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.323 |
|
| \begin{align*}
y^{\prime }-2 y x&=-1 \\
y \left (0\right ) &= \frac {\sqrt {\pi }}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
y^{\prime }+y \,{\mathrm e}^{x}&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \begin{align*}
x^{2} y^{\prime }-y&=x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.612 |
|
| \begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.129 |
|
| \begin{align*}
y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.741 |
|
| \begin{align*}
x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.816 |
|
| \begin{align*}
x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.930 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.266 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) \left (x +1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.543 |
|
| \begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.156 |
|
| \begin{align*}
y^{\prime }+y&=2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.259 |
|
| \begin{align*}
y^{\prime }+\frac {x +2 y}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.204 |
|
| \begin{align*}
x y^{\prime }&=x +\frac {y}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
40.325 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (x \right ) \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.236 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2}+x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.631 |
|
| \begin{align*}
y+3 y^{\prime }&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.731 |
|
| \begin{align*}
y^{\prime }+3 y&={\mathrm e}^{i x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.418 |
|
| \begin{align*}
y^{\prime }+i y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
L y^{\prime }+R y&=E \sin \left (\omega x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.445 |
|
| \begin{align*}
y^{\prime }+a y&=b \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
x y^{\prime }+y&=3 x^{3}-1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.779 |
|
| \begin{align*}
y^{\prime }+y \,{\mathrm e}^{x}&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.644 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&={\mathrm e}^{\sin \left (x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.435 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.674 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \\
y \left (\pi \right ) &= \pi \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
2 y+y^{\prime }&=b \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.063 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.090 |
|
| \begin{align*}
y^{\prime }&=1+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.241 |
|
| \begin{align*}
y^{\prime }&=4 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.006 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.736 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.283 |
|
| \begin{align*}
y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
y^{\prime }+y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.275 |
|
| \begin{align*}
2 y-x^{3}&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
y^{\prime }-y x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=2 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
x y^{\prime }&=2 x^{2} y+y \ln \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.890 |
|
| \begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
8.355 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| \begin{align*}
x y^{\prime }&=2 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.120 |
|
| \begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.053 |
|
| \begin{align*}
x y^{\prime }+y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.796 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.766 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.743 |
|
| \begin{align*}
x y^{\prime }-y&=2 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.492 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y&=3 x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.094 |
|
| \begin{align*}
\frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.963 |
|
| \begin{align*}
y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.616 |
|
| \begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.616 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.513 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.579 |
|
| \begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.912 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.665 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.426 |
|
| \begin{align*}
x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.479 |
|
| \begin{align*}
y^{\prime }&=x +\frac {\sec \left (x \right ) y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.180 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
8.431 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.559 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
122.758 |
|
| \begin{align*}
y^{\prime }&=a x y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.480 |
|
| \begin{align*}
y^{\prime }&=a x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
y^{\prime }&=a x +b y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
c y^{\prime }&=a x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
c y^{\prime }&=a x +b y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| \begin{align*}
y^{\prime }+a y-c \,{\mathrm e}^{b x}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
y^{\prime }+a y-b \sin \left (c x \right )&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.930 |
|
| \begin{align*}
y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.603 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y-\frac {\sin \left (2 x \right )}{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.669 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{-\sin \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )-\sin \left (2 x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.401 |
|
| \begin{align*}
y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.695 |
|
| \begin{align*}
y^{\prime }+f^{\prime }\left (x \right ) y-f \left (x \right ) f^{\prime }\left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) y-g \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.640 |
|
| \begin{align*}
x y^{\prime }+y-x \sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.902 |
|
| \begin{align*}
x y^{\prime }-y-\frac {x}{\ln \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.379 |
|
| \begin{align*}
x y^{\prime }-y-x^{2} \sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| \begin{align*}
x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.718 |
|
| \begin{align*}
x y^{\prime }+a y+b \,x^{n}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.197 |
|
| \begin{align*}
2 x y^{\prime }-y-2 x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.679 |
|
| \begin{align*}
x^{2} y^{\prime }+y-x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.601 |
|
| \begin{align*}
x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.246 |
|
| \begin{align*}
x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.441 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.357 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y x +a&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.528 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.233 |
|
| \begin{align*}
\left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.294 |
|
| \begin{align*}
\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.330 |
|
| \begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.147 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.800 |
|
| \begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.269 |
|
| \begin{align*}
\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
18.373 |
|
| \begin{align*}
y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.617 |
|
| \begin{align*}
g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{0} \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| \begin{align*}
y^{\prime }&=a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.191 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.507 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.255 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.691 |
|
| \begin{align*}
\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.173 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.688 |
|
| \begin{align*}
x y^{\prime }-y+2 x^{2} y-x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.458 |
|
| \begin{align*}
y^{\prime }-x^{2} y&=x^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.277 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
13.203 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.521 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.268 |
|
| \begin{align*}
x^{\prime }+2 x&=t^{2}+4 t +7 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.203 |
|
| \begin{align*}
2 x^{\prime } t&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.815 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.390 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \begin{align*}
x^{\prime }&=2 t^{3} x-6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.870 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{t}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.506 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
x^{\prime }+2 x t&={\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| \begin{align*}
x^{\prime } t&=-x+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-3 x t +6 t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.000 |
|
| \begin{align*}
x^{\prime }+\frac {5 x}{t}&=t +1 \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.203 |
|
| \begin{align*}
x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.264 |
|
| \begin{align*}
R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\
R \left (1\right ) &= 3 \ln \left (2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.471 |
|
| \begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
\cos \left (\theta \right ) v^{\prime }+v&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.405 |
|
| \begin{align*}
R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\
R \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.690 |
|
| \begin{align*}
y^{\prime }+a y&=\sqrt {t +1} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| \begin{align*}
x^{\prime }&=2 x t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.854 |
|
| \begin{align*}
x^{\prime }+\frac {{\mathrm e}^{-t} x}{t}&=t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.755 |
|
| \begin{align*}
x^{\prime }+p \left (t \right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.874 |
|
| \begin{align*}
y^{\prime }+y&=x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.906 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.443 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.292 |
|
| \begin{align*}
2 y+y^{\prime }&=6 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.574 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\
y \left (-1\right ) &= {\mathrm e}+3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.255 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.103 |
|
| \begin{align*}
y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.437 |
|
| \begin{align*}
x +y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.654 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.851 |
|
| \begin{align*}
x^{4} y^{\prime }+2 x^{3} y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.833 |
|
| \begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.289 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.124 |
|
| \begin{align*}
x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.630 |
|
| \begin{align*}
\left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.472 |
|
| \begin{align*}
x y^{\prime }+\frac {\left (2 x +1\right ) y}{x +1}&=x -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.377 |
|
| \begin{align*}
\left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y&=x -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.560 |
|
| \begin{align*}
x y^{\prime }+y x +y-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.945 |
|
| \begin{align*}
r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.564 |
|
| \begin{align*}
\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.888 |
|
| \begin{align*}
\cos \left (x \right )^{2}-\cos \left (x \right ) y-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.155 |
|
| \begin{align*}
y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.953 |
|
| \begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.638 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y-3 \left (1+{\mathrm e}^{x}\right )^{2}\right )+\left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.740 |
|
| \begin{align*}
2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.355 |
|
| \begin{align*}
r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\
r \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.994 |
|
| \begin{align*}
x^{\prime }-x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.050 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.534 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\
y \left (0\right ) &= 6 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.660 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.909 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.254 |
|
| \begin{align*}
a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.646 |
|
| \begin{align*}
y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.639 |
|
| \begin{align*}
6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.363 |
|
| \begin{align*}
y-1+x \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.804 |
|
| \begin{align*}
x^{2}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.492 |
|
| \begin{align*}
8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.787 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y x&={\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.536 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{x^{2}+1} \\
y \left (\sqrt {15}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.770 |
|
| \begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.759 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.931 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \begin{align*}
x^{\prime }&=t^{3} \left (1-x\right ) \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.209 |
|
| \begin{align*}
x^{\prime }&=x t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.314 |
|
| \begin{align*}
x y^{\prime }&=k y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.968 |
|
| \begin{align*}
i^{\prime }&=p \left (t \right ) i \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.189 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.553 |
|
| \begin{align*}
x^{\prime }+x t&=4 t \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.193 |
|
| \begin{align*}
z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.133 |
|
| \begin{align*}
y^{\prime }+{\mathrm e}^{-x} y&=1 \\
y \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.690 |
|
| \begin{align*}
x^{\prime }+x \tanh \left (t \right )&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.190 |
|
| \begin{align*}
y^{\prime }+2 y \cot \left (x \right )&=5 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.418 |
|
| \begin{align*}
x^{\prime }+5 x&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.521 |
|
| \begin{align*}
x^{\prime }+\left (a +\frac {1}{t}\right ) x&=b \\
x \left (1\right ) &= x_{0} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.708 |
|
| \begin{align*}
T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.530 |
|
| \begin{align*}
1+y \,{\mathrm e}^{x}+y x \,{\mathrm e}^{x}+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.309 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.946 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.907 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.791 |
|
| \begin{align*}
x^{\prime }&=x+\sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.396 |
|
| \begin{align*}
x^{\prime }+5 x&=10 t +2 \\
x \left (1\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.079 |
|
| \begin{align*}
x^{\prime }-x \cot \left (t \right )&=4 \sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.422 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.096 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=\sinh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
30.003 |
|
| \begin{align*}
5 y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.583 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.198 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.102 |
|
| \begin{align*}
1+y-\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.510 |
|
| \begin{align*}
y-a +x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.507 |
|
| \begin{align*}
z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.735 |
|
| \begin{align*}
r^{\prime }+r \tan \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.925 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.452 |
|
| \begin{align*}
t -s+t s^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.657 |
|
| \begin{align*}
x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.358 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.966 |
|
| \begin{align*}
y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.880 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.187 |
|
| \begin{align*}
s^{\prime } \cos \left (t \right )+s \sin \left (t \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.000 |
|
| \begin{align*}
s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.288 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.590 |
|
| \begin{align*}
y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.707 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.025 |
|
| \begin{align*}
y&=x y^{\prime }+y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.948 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.579 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-y x -\alpha &=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.287 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&={\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.314 |
|
| \begin{align*}
x y^{\prime }-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.606 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.713 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.433 |
|
| \begin{align*}
2 x y^{\prime }-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.534 |
|
| \begin{align*}
y^{\prime }-2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.058 |
|
| \begin{align*}
y^{\prime }+y&=x^{2}+2 x -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.802 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.199 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.401 |
|
| \begin{align*}
y^{\prime }&=-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.827 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.339 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.168 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.685 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.828 |
|
| \begin{align*}
y^{\prime }&=y x +\frac {1}{x^{2}+1} \\
y \left (-5\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.418 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.744 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.708 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.150 |
|
| \begin{align*}
y^{\prime }&=y \cot \left (x \right )+\csc \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.261 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.307 |
|
| \begin{align*}
y^{\prime }&=y x +x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.993 |
|
| \begin{align*}
y-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.286 |
|
| \begin{align*}
y^{\prime }&=\frac {-y x +1}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.907 |
|
| \begin{align*}
y^{\prime }&=y x +2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.490 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.261 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -1}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.614 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.562 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+{\mathrm e}^{x} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.497 |
|
| \begin{align*}
y^{\prime }&=y \cot \left (x \right )+\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.987 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.597 |
|
| \begin{align*}
\left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.840 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.222 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.630 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.243 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.896 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.613 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
8.669 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.535 |
|
| \begin{align*}
y^{\prime }&=t^{4} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.460 |
|
| \begin{align*}
v^{\prime }&=t^{2} v-2-2 v+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.952 |
|
| \begin{align*}
w^{\prime }&=\frac {w}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
x^{\prime }&=-x t \\
x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.826 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.709 |
|
| \begin{align*}
y^{\prime }&=t +y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
y^{\prime }&=2 y-t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
y^{\prime }&=\left (t +1\right ) y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.912 |
|
| \begin{align*}
y^{\prime }&=t^{2}+t^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| \begin{align*}
y^{\prime }&=t +y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
v^{\prime }&=2 V \left (t \right )-2 v \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.760 |
|
| \begin{align*}
y^{\prime }&=-4 y+9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.595 |
|
| \begin{align*}
y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.112 |
|
| \begin{align*}
y^{\prime }&=2 y+\sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| \begin{align*}
y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.600 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 10 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
3 y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| \begin{align*}
-2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \begin{align*}
y^{\prime }+2 y&=3 t^{2}+2 t -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.441 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
y+y^{\prime }&=t^{3}+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.400 |
|
| \begin{align*}
y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.729 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.832 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{t}+t^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.984 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.707 |
|
| \begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.272 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.934 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.424 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.873 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.128 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.854 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| \begin{align*}
y^{\prime }&=y+4 \cos \left (t^{2}\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.585 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\sqrt {t^{3}-3}}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
74.306 |
|
| \begin{align*}
y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \begin{align*}
y^{\prime }&=t^{r} y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.183 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.282 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \begin{align*}
y^{\prime }&=y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{7 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{t^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| \begin{align*}
y^{\prime }&=-5 y+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| \begin{align*}
y^{\prime }&=t +\frac {2 y}{t +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| \begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| \begin{align*}
x^{\prime }&=-x t \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.967 |
|
| \begin{align*}
y^{\prime }&=2 y+\cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.622 |
|
| \begin{align*}
y^{\prime }&=3 y+2 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \begin{align*}
y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \begin{align*}
y^{\prime }&=2 y t +3 t \,{\mathrm e}^{t^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.101 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+1+y+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.130 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.849 |
|
| \begin{align*}
y^{\prime }+3 y x&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.857 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }&=y+3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.224 |
|
| \begin{align*}
y^{\prime }&=3 x -y \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| \begin{align*}
y^{\prime }+y x&=4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| \begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.221 |
|
| \begin{align*}
y^{\prime }&=2 x -1+2 y x -y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| \begin{align*}
y^{\prime }&=y x -4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
y^{\prime }&=y x -4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.853 |
|
| \begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.159 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
y^{\prime }&=2 x -1+2 y x -y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
x^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
y^{\prime }&=1+y x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.194 |
|
| \begin{align*}
x y^{\prime }+\cos \left (x^{2}\right )&=827 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
12.557 |
|
| \begin{align*}
2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y^{\prime }&=4 y+16 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.818 |
|
| \begin{align*}
x y^{\prime }+3 y-10 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.859 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.569 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=\cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \begin{align*}
x y^{\prime }+\left (2+5 x \right ) y&=\frac {20}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }+y&=2 x \,{\mathrm e}^{-\sqrt {x}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.905 |
|
| \begin{align*}
y^{\prime }+5 y&={\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| \begin{align*}
x y^{\prime }+3 y&=20 x^{2} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.948 |
|
| \begin{align*}
x y^{\prime }&=y+x^{2} \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3+3 x^{2}-y\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.776 |
|
| \begin{align*}
y^{\prime }+6 y x&=\sin \left (x \right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.515 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\sqrt {x}\, \sin \left (x \right ) \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.708 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} {\mathrm e}^{-x^{2}} \\
y \left (3\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
2 x \left (y+1\right )-y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
x y^{\prime }&=2 y-6 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.139 |
|
| \begin{align*}
4 y x -6+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| \begin{align*}
3 y-x^{3}+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.718 |
|
| \begin{align*}
2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.788 |
|
| \begin{align*}
y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| \begin{align*}
2 y-6 x +\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.208 |
|
| \begin{align*}
2 y+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| \begin{align*}
y^{\prime }&=x \left (6 y+{\mathrm e}^{x^{2}}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.295 |
|
| \begin{align*}
x^{2} y^{\prime }+3 y x&=6 \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.579 |
|
| \begin{align*}
x y^{\prime }+3 y&={\mathrm e}^{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.482 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x}-3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.155 |
|
| \begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.417 |
|
| \begin{align*}
x y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.360 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.215 |
|
| \begin{align*}
2 y+y^{\prime }&=x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.917 |
|
| \begin{align*}
y^{\prime }&=y+\frac {1}{1-t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {t} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.573 |
|
| \begin{align*}
t y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| \begin{align*}
t y^{\prime }+y&=t^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.173 |
|
| \begin{align*}
t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| \begin{align*}
2 y^{\prime }+y t&=\ln \left (t \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.732 |
|
| \begin{align*}
y^{\prime }+y \sec \left (t \right )&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.243 |
|
| \begin{align*}
y^{\prime }+\frac {y}{-3+t}&=\frac {1}{t -1} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.842 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.964 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.776 |
|
| \begin{align*}
t y^{\prime }+y&=t \sin \left (t \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.571 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.175 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{2 t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.402 |
|
| \begin{align*}
y^{\prime }&=\frac {y+3}{1+3 x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.800 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y+1}{x +3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.253 |
|
| \begin{align*}
y^{\prime }&=\cos \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.866 |
|
| \begin{align*}
y^{\prime }+y f \left (t \right )&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.640 |
|
| \begin{align*}
y^{\prime }&=-\frac {-2+y}{x -2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.931 |
|
| \begin{align*}
y^{\prime }&=y f \left (t \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.602 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.454 |
|
| \begin{align*}
-y+y^{\prime }&=2 \cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.467 |
|
| \begin{align*}
-y+y^{\prime }&=t^{2}-2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.294 |
|
| \begin{align*}
-y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
t y^{\prime }+y&=t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.981 |
|
| \begin{align*}
t y^{\prime }+y&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.460 |
|
| \begin{align*}
x y^{\prime }+y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
x y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.476 |
|
| \begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.206 |
|
| \begin{align*}
y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.884 |
|
| \begin{align*}
y^{\prime }&=2 x +\frac {x y}{x^{2}-1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.337 |
|
| \begin{align*}
y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.973 |
|
| \begin{align*}
y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.444 |
|
| \begin{align*}
y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.191 |
|
| \begin{align*}
y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.408 |
|
| \begin{align*}
y^{\prime }+2 y \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.590 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \begin{align*}
y^{\prime }-x&=y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.919 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| \begin{align*}
p^{\prime }&=t^{3}+\frac {p}{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.092 |
|
| \begin{align*}
v^{\prime }+v&={\mathrm e}^{-s} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.043 |
|
| \begin{align*}
-y+y^{\prime }&=4 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.262 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.431 |
|
| \begin{align*}
2 y t +y^{\prime }&=2 t \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.877 |
|
| \begin{align*}
t y^{\prime }+y&=\cos \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= \frac {4}{\pi } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.870 |
|
| \begin{align*}
t y^{\prime }+y&=2 \,{\mathrm e}^{t} t \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y&=t \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.057 |
|
| \begin{align*}
\left (t^{2}+4\right ) y^{\prime }+2 y t&=2 t \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.168 |
|
| \begin{align*}
x^{\prime }&=x+t +1 \\
x \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.975 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.050 |
|
| \begin{align*}
-y+y^{\prime }&=\sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \begin{align*}
y+y^{\prime }&=2-{\mathrm e}^{2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }-5 y&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.085 |
|
| \begin{align*}
3 y+y^{\prime }&=27 t^{2}+9 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.755 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.150 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \cos \left (4 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| \begin{align*}
y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y^{\prime }-3 y&=27 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.116 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.923 |
|
| \begin{align*}
y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
y+y^{\prime }&=2 \cos \left (t \right )+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.765 |
|
| \begin{align*}
\frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.524 |
|
| \begin{align*}
t y^{\prime }+y&=\cos \left (t \right ) t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| \begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.145 |
|
| \begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.610 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| \begin{align*}
\sec \left (t \right )^{2} y+2 t +\tan \left (t \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
13.272 |
|
| \begin{align*}
{\mathrm e}^{y t}+\frac {t \,{\mathrm e}^{y t} y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.341 |
|
| \begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.079 |
|
| \begin{align*}
1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.077 |
|
| \begin{align*}
2 y t +3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.531 |
|
| \begin{align*}
t^{2} y+t^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.017 |
|
| \begin{align*}
y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.483 |
|
| \begin{align*}
2 y-3 t +t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.910 |
|
| \begin{align*}
t -y+t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| \begin{align*}
t +y-t y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.550 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.453 |
|
| \begin{align*}
y&=t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.891 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.687 |
|
| \begin{align*}
3 y+y^{\prime }&=-10 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| \begin{align*}
y-x +y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \begin{align*}
y t +y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.513 |
|
| \begin{align*}
x^{\prime }+\frac {x}{y}&=y^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.079 |
|
| \begin{align*}
t r^{\prime }+r&=\cos \left (t \right ) t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t -2} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| \begin{align*}
y^{\prime }-4 y&=t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.975 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
y^{\prime }+4 y&=t \,{\mathrm e}^{-4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.636 |
|
| \begin{align*}
x y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.872 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.720 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.140 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.277 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.790 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| \begin{align*}
y^{\prime }&=2 y-2 x^{2}-3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.158 |
|
| \begin{align*}
x y^{\prime }&=2 x -y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.273 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.650 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.668 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (y x +1\right ) \\
y \left (\frac {1}{a}\right ) &= -a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.249 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.576 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.640 |
|
| \begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.585 |
|
| \begin{align*}
x -y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
x +y-2+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.144 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| \begin{align*}
x^{2}-x y^{\prime }&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.442 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.595 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=2 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| \begin{align*}
x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.251 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=\frac {1}{\cos \left (x \right )^{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.142 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=3 x^{3} \ln \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.230 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.025 |
|
| \begin{align*}
y^{\prime }-y \,{\mathrm e}^{x}&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| \begin{align*}
y^{\prime }+y x \,{\mathrm e}^{x}&={\mathrm e}^{{\mathrm e}^{x} \left (1-x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.938 |
|
| \begin{align*}
y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| \begin{align*}
y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=-\frac {\sin \left (x \right )^{2}}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.546 |
|
| \begin{align*}
x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right )&=-1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.211 |
|
| \begin{align*}
2 x y^{\prime }-y&=1-\frac {2}{\sqrt {x}} \\
y \left (\infty \right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
35.088 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\
y \left (-\infty \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✗ |
✓ |
3.957 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.793 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.638 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=-\sin \left (2 x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.121 |
|
| \begin{align*}
y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.844 |
|
| \begin{align*}
\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
38.215 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.316 |
|
| \begin{align*}
2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.868 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y&=\sin \left (x \right ) \cos \left (x \right )-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.776 |
|
| \begin{align*}
2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.278 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.888 |
|
| \begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.913 |
|
| \begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.810 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.958 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.550 |
|
| \begin{align*}
y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.766 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=5+\cos \left (2 t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.268 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.319 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| \begin{align*}
2 y t +y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.694 |
|
| \begin{align*}
4 y t +\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.166 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
-y+t y^{\prime }&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.401 |
|
| \begin{align*}
y+y^{\prime }&=5 \sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.644 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| \begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.680 |
|
| \begin{align*}
t y^{\prime }+4 y&=t^{2}-t +1 \\
y \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.578 |
|
| \begin{align*}
\frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.759 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.747 |
|
| \begin{align*}
4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.780 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=t \\
y \left (\ln \left (2\right )\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| \begin{align*}
y^{\prime }-\frac {y}{3}&=3 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| \begin{align*}
-y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.565 |
|
| \begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.290 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.724 |
|
| \begin{align*}
2 y+t y^{\prime }&=\frac {\sin \left (t \right )}{t} \\
y \left (-\frac {\pi }{2}\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.865 |
|
| \begin{align*}
\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
27.957 |
|
| \begin{align*}
\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.380 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.924 |
|
| \begin{align*}
\frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.831 |
|
| \begin{align*}
-y+y^{\prime }&=1+3 \sin \left (t \right ) \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.421 |
|
| \begin{align*}
-\frac {3 y}{2}+y^{\prime }&=3 t +3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.788 |
|
| \begin{align*}
y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.636 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.145 |
|
| \begin{align*}
2 y+t y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.453 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.141 |
|
| \begin{align*}
\ln \left (t \right ) y+\left (-3+t \right ) y^{\prime }&=2 t \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
10.059 |
|
| \begin{align*}
y+\left (-4+t \right ) t y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.140 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.911 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.038 |
|
| \begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.836 |
|
| \begin{align*}
y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.557 |
|
| \begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.632 |
|
| \begin{align*}
y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.890 |
|
| \begin{align*}
\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.625 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| \begin{align*}
\frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.043 |
|
| \begin{align*}
\left (2-x \right ) y^{\prime }&=y+2 \left (2-x \right )^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.840 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )+\cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
y^{\prime }&=2 y x -x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.397 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
y^{\prime }&=k y+f \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.764 |
|
| \begin{align*}
y^{\prime }&=2 y x -x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.580 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.875 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.894 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.971 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.000 |
|
| \begin{align*}
y^{\prime }&=1+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.765 |
|
| \begin{align*}
x y^{\prime }&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.095 |
|
| \begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.332 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2}-3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.449 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.832 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.249 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.954 |
|
| \begin{align*}
2 y-x^{3}&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.437 |
|
| \begin{align*}
y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.209 |
|
| \begin{align*}
y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.973 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.164 |
|
| \begin{align*}
y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.874 |
|
| \begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.289 |
|
| \begin{align*}
x^{2}+y&=x y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.366 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.153 |
|
| \begin{align*}
y^{\prime }&=1+3 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
\frac {-x +y}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.189 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.309 |
|
| \begin{align*}
x y^{\prime }+y x +y-1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
x^{\prime }+x \cot \left (y \right )&=\sec \left (y \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.307 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.706 |
|
| \begin{align*}
x^{\prime }+2 x&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \begin{align*}
x^{\prime }+x \tan \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| \begin{align*}
x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.733 |
|
| \begin{align*}
t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.023 |
|
| \begin{align*}
x^{\prime } t +x \ln \left (t \right )&=t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.036 |
|
| \begin{align*}
x^{\prime } t +x g \left (t \right )&=h \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.384 |
|
| \begin{align*}
v^{\prime }+u^{2} v&=\sin \left (u \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.462 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.443 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
y^{\prime }+y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| \begin{align*}
p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.110 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 v \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
\frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.787 |
|
| \begin{align*}
v^{\prime }+2 u v&=2 u \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.153 |
|
| \begin{align*}
5 x^{\prime }+x&=\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\csc \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.371 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x^{2} y&=x^{3}-x^{2} \arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.666 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.023 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.280 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }-y-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.862 |
|
| \begin{align*}
y-x y^{\prime }+\ln \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| \begin{align*}
x y^{\prime }-a y&=x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.392 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
\cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.191 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-n y&={\mathrm e}^{x} \left (x +1\right )^{n +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.118 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.418 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
9.050 |
|
| \begin{align*}
y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+y&=\sqrt {a^{2}+x^{2}}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.590 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.748 |
|
| \begin{align*}
y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.123 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.246 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.457 |
|
| \begin{align*}
x y^{\prime }-y-\cos \left (\frac {1}{x}\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.660 |
|
| \begin{align*}
2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.696 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| \begin{align*}
\cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.773 |
|
| \begin{align*}
x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.414 |
|
| \begin{align*}
y-x \sin \left (x^{2}\right )+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.279 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=2 \ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=\sin \left (x \right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.062 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=x^{5} {\mathrm e}^{x^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.093 |
|
| \begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.238 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| \begin{align*}
1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.138 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.895 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.691 |
|
| \begin{align*}
y&=\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.128 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.834 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| \begin{align*}
x y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.163 |
|
| \begin{align*}
s^{\prime }+2 s&=s t^{2} \\
s \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.470 |
|
| \begin{align*}
x^{\prime }-2 x&={\mathrm e}^{2 t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.697 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{3} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.777 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.760 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.488 |
|
| \begin{align*}
y&=x y^{\prime }+a y^{\prime }+b \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.944 |
|
| \begin{align*}
x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5}&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
32.652 |
|
| \begin{align*}
x^{\prime }-2 x \cos \left (t \right )&=\cos \left (t \right ) \\
x \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.665 |
|
| \begin{align*}
x^{\prime }+\frac {x}{t^{2}-1}&=0 \\
x \left (-2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.472 |
|
| \begin{align*}
x^{\prime }+\sec \left (t \right ) x&=\frac {1}{t -1} \\
x \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.264 |
|
| \begin{align*}
x^{\prime } t +x&=2 t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
t^{2} x^{\prime }-2 x t&=t^{5} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.832 |
|
| \begin{align*}
x^{\prime }&=2 x t \\
x \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.064 |
|
| \begin{align*}
x^{\prime }&=-x t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.046 |
|
| \begin{align*}
x^{\prime }+a x&=b t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| \begin{align*}
x^{\prime }&=x+2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
x^{\prime }-2 x&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.927 |
|
| \begin{align*}
x^{\prime }+3 x&=-2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
x^{\prime }+a x&=b t \\
x \left (t_{0} \right ) &= x_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
x^{\prime }-x&=\frac {t}{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| \begin{align*}
x^{\prime }+x&=4 t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.493 |
|
| \begin{align*}
x^{\prime }-2 x&=2 t \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t^{2}+1} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.264 |
|
| \begin{align*}
x^{\prime }+2 x&=6 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
x^{\prime }+x&=a t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| \begin{align*}
x^{\prime }+\frac {\sin \left (t \right ) x}{1+{\mathrm e}^{t}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.748 |
|
| \begin{align*}
x^{\prime }&=x t -t^{3} \\
x \left (a \right ) &= a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.918 |
|
| \begin{align*}
x^{\prime }&=x t -t^{3} \\
x \left (0\right ) &= a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
2 y+x +\left (x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| \begin{align*}
x +2 y+\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \begin{align*}
x^{\prime }&=\frac {x+2 t}{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| \begin{align*}
x&=t \left (1+x^{\prime }\right )+x^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
x y^{\prime }-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.565 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.042 |
|
| \begin{align*}
x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.542 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.783 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.405 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.319 |
|
| \begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.922 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.442 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.988 |
|
| \begin{align*}
y^{\prime }-y x&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.327 |
|
| \begin{align*}
y^{\prime }+\tan \left (\theta \right ) y&=\cos \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.925 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.225 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.425 |
|
| \begin{align*}
x^{\prime }-x \tan \left (t \right )&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.951 |
|
| \begin{align*}
y^{\prime }&=2 y x -x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.800 |
|
| \begin{align*}
y^{\prime }+\left (b x +a \right ) y&=f \left (x \right ) \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
2 y-8 x^{2}+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.802 |
|
| \begin{align*}
\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| \begin{align*}
y^{\prime }+q \left (x \right ) y&=0 \\
y \left (\textit {x\_0} \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.694 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.159 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.748 |
|
| \begin{align*}
y^{\prime }+y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.792 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| \begin{align*}
y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.033 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.302 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}+2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.164 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.718 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
y^{\prime }-y&=3 x^{2}+x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.392 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.805 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{3}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.223 |
|
| \begin{align*}
y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.809 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.917 |
|
| \begin{align*}
x y^{\prime }&=x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.105 |
|
| \begin{align*}
y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.429 |
|
| \begin{align*}
r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.407 |
|
| \begin{align*}
r^{\prime }&=r \tan \left (t \right ) \\
r \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.412 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{2} y&=x^{5} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.023 |
|
| \begin{align*}
x y^{\prime }+y&=3 x^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.318 |
|
| \begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=2 x \,{\mathrm e}^{\cos \left (x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=8 x^{2} \cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.048 |
|
| \begin{align*}
2 y+y^{\prime }&=\sin \left (3 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.964 |
|
| \begin{align*}
2+3 x -5 y+7 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
y^{\prime }+3 x^{2} y&=3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.785 |
|
| \begin{align*}
\left (x^{3}+3\right ) y^{\prime }+2 y x +5 x^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
50.286 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right )+{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.127 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.139 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y}{x^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.469 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.540 |
|
| \begin{align*}
y^{\prime }&=y x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.689 |
|
| \begin{align*}
\frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.012 |
|
| \begin{align*}
x +\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.390 |
|
| \begin{align*}
x^{2}+1+\frac {y^{\prime }}{y}&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.925 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.167 |
|
| \begin{align*}
y^{\prime }&=y x \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.579 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.142 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.772 |
|
| \begin{align*}
y x +x^{2}-y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (2\right ) &= -5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.274 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.616 |
|
| \begin{align*}
y \sin \left (x \right )+y \cos \left (x \right ) x +\left (x \sin \left (x \right )+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.178 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.888 |
|
| \begin{align*}
y^{\prime }&=2 y x -x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.969 |
|
| \begin{align*}
y+1-x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.685 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.601 |
|
| \begin{align*}
3 x^{2} y-x^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.967 |
|
| \begin{align*}
3 x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.817 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.922 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.181 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.958 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \begin{align*}
y^{\prime }-7 y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| \begin{align*}
y^{\prime }-7 y&=14 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.733 |
|
| \begin{align*}
y^{\prime }-7 y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.232 |
|
| \begin{align*}
y^{\prime }+x^{2} y&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.388 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.503 |
|
| \begin{align*}
y^{\prime }+6 y x&=0 \\
y \left (\pi \right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.045 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.180 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.579 |
|
| \begin{align*}
3 y^{\prime }+y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.371 |
|
| \begin{align*}
y^{\prime }-2 y&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.350 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.093 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| \begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.790 |
|
| \begin{align*}
y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.469 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.542 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.373 |
|
| \begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.800 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.229 |
|
| \begin{align*}
y^{\prime }&=x^{2}+5 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.076 |
|
| \begin{align*}
2 x +y+\left (x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.756 |
|
| \begin{align*}
y^{\prime }+y&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| \begin{align*}
y^{\prime }&=1+2 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.973 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.898 |
|
| \begin{align*}
y^{\prime }&=3 x +2 y \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \begin{align*}
y^{\prime }+y x&=x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.109 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.937 |
|
| \begin{align*}
2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.045 |
|
| \begin{align*}
2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.782 |
|
| \begin{align*}
y^{\prime }&=8 y x +3 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.680 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.932 |
|
| \begin{align*}
x y^{\prime }&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.427 |
|
| \begin{align*}
x -4 y+\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.720 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.926 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-2 y \sin \left (x \right )+3&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.970 |
|
| \begin{align*}
2 x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| \begin{align*}
2 y \sin \left (x \right )-\cos \left (x \right )^{3}+\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.549 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.408 |
|
| \begin{align*}
i^{\prime }&=\frac {t -i t}{t^{2}+1} \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.033 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.667 |
|
| \begin{align*}
3 x^{2}+y+3 x^{3} y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.723 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.799 |
|
| \begin{align*}
x y^{\prime }+3 y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.572 |
|
| \begin{align*}
i^{\prime }+3 i&={\mathrm e}^{-2 t} \\
i \left (0\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.990 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
r^{\prime }&=t -\frac {r}{3 t} \\
r \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.527 |
|
| \begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.843 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.810 |
|
| \begin{align*}
3-y+2 x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.102 |
|
| \begin{align*}
y^{\prime }&=\left (2 x^{2}-y \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.148 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.569 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.279 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.457 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=\cos \left (x \right ) y+\sin \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.500 |
|
| \begin{align*}
2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.259 |
|
| \begin{align*}
x +2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.080 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.792 |
|
| \begin{align*}
2 y+3 x +x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.392 |
|
| \begin{align*}
x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.542 |
|
| \begin{align*}
i^{\prime }+i&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.741 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.770 |
|
| \begin{align*}
y^{\prime }&=3 x +2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.957 |
|
| \begin{align*}
u^{\prime }&=-a \left (u-100 t \right ) \\
u \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.536 |
|
| \begin{align*}
u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.099 |
|
| \begin{align*}
i^{\prime }+3 i&=10 \sin \left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.609 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.437 |
|
| \begin{align*}
x y^{\prime }-3 y&=x^{4} {\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.204 |
|
| \begin{align*}
y^{\prime }&=2-\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.964 |
|
| \begin{align*}
r^{\prime }&={\mathrm e}^{t}-3 r \\
r \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.569 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }&=y-\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.352 |
|
| \begin{align*}
2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.955 |
|
| \begin{align*}
x y^{\prime }+2 y-x \cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| \begin{align*}
y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.723 |
|
| \begin{align*}
y^{\prime }&=x \left (x +y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.187 |
|
| \begin{align*}
y^{\prime }+y x&=x^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.901 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.496 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.490 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.656 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.425 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.985 |
|
| \begin{align*}
x y^{\prime }-1+y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.740 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.663 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
\frac {y}{x}+\ln \left (x \right ) y^{\prime }&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.052 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.797 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.687 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+2}{x +1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.246 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.365 |
|
| \begin{align*}
y^{\prime }-2 y x&=3 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.562 |
|
| \begin{align*}
y^{\prime }+7 y&={\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.307 |
|
| \begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.596 |
|
| \begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.153 |
|
| \begin{align*}
z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\
z \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
26.236 |
|
| \begin{align*}
z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\
z \left (2 \pi \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.707 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=5 x \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.053 |
|
| \begin{align*}
y^{\prime }-\frac {6 y}{x}&=7 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.011 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.093 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{x}&={\mathrm e}^{x} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.290 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\
y \left (0\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.497 |
|
| \begin{align*}
n^{\prime }&=k n-b t \\
n \left (0\right ) &= n_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.663 |
|
| \begin{align*}
x y^{\prime }-2 \cos \left (x \right ) y&={\mathrm e}^{x} \sin \left (x \right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
29.998 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3} \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.862 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +a^{2}}{a^{2}-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
y^{\prime }+\frac {y \ln \left (x \right )}{x}&=2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.564 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{k x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.975 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.948 |
|
| \begin{align*}
v^{\prime }&=60 t -4 v \\
v \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
\frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.847 |
|
| \begin{align*}
\left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| \begin{align*}
\cot \left (\theta \right ) r^{\prime }&=r+b \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right )&=0 \\
r \left (\frac {\pi }{2}\right ) &= 2 a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.185 |
|
| \begin{align*}
r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.280 |
|
| \begin{align*}
y^{\prime }-2 y&={\mathrm e}^{x} \left (1-x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.940 |
|
| \begin{align*}
y^{\prime }+y x&=3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \begin{align*}
x y^{\prime }+\frac {y}{2 x +3}&=\ln \left (x -2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
x y^{\prime }-y&=1 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| \begin{align*}
y^{\prime }-y x&=-x^{2}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
y^{\prime }&=y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.414 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.110 |
|
| \begin{align*}
y^{\prime }+y x&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.424 |
|
| \begin{align*}
y^{\prime }&=x -y x -y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.427 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-x +a \right ) y}{d \,x^{2}+c x +b} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.235 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
x y^{\prime }+y&=3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
x y^{\prime }-y&=2 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.008 |
|
| \begin{align*}
x y^{\prime }+6 y&=1+3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
{\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| \begin{align*}
x y^{\prime }+y&=x^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.577 |
|
| \begin{align*}
y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
y^{\prime }-y x&=\left (-x^{2}+1\right ) {\mathrm e}^{\frac {x^{2}}{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.380 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.275 |
|
| \begin{align*}
x y^{\prime }-\frac {y}{\ln \left (x \right )}&=0 \\
y \left ({\mathrm e}\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.324 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.950 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }+y x&=x \left (x -1\right )^{2} \\
y \left (5\right ) &= 24 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.925 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\
y \left (-1\right ) &= 16 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| \begin{align*}
y^{\prime }-2 y x&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| \begin{align*}
x^{2}-2 y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.394 |
|
| \begin{align*}
y-2 x -x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.743 |
|
| \begin{align*}
5 x -y+3 x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.467 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.602 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.052 |
|
| \begin{align*}
7 y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.894 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| \begin{align*}
y^{\prime }&=t +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
4 y+3 x y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| \begin{align*}
2 x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.658 |
|
| \begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| \begin{align*}
y x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.756 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} y-3 x^{4}+2 x^{2}-2 y+2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
y^{\prime }&=1+\frac {3 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.134 |
|
| \begin{align*}
x^{4}-3 y+3 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.368 |
|
| \begin{align*}
2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| \begin{align*}
y^{\prime }+3 y&=x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
y^{\prime }-2 y&=\cos \left (3 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.357 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.537 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| \begin{align*}
y^{\prime }+x^{2} y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.402 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.387 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=\sin \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
y^{\prime }-\frac {y}{-x^{2}+1}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.175 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.717 |
|
| \begin{align*}
y^{\prime }-y x&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.819 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.289 |
|
| \begin{align*}
y^{\prime }-2 y&=x^{2}-1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.440 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{2}&=x^{4} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.383 |
|
| \begin{align*}
y^{\prime }-5 y&=3 x^{3}+4 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.905 |
|
| \begin{align*}
y^{\prime }-y x&=-x^{5}+4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.097 |
|
| \begin{align*}
2 y-3 x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.426 |
|
| \begin{align*}
m y-n x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.055 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{p} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.933 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.441 |
|
| \begin{align*}
y x -\left (x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.654 |
|
| \begin{align*}
y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.401 |
|
| \begin{align*}
r^{\prime }&=-2 r t \\
r \left (0\right ) &= r_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.689 |
|
| \begin{align*}
2 x y \cos \left (x^{2}\right )-2 y x +1+\left (\sin \left (x^{2}\right )-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.864 |
|
| \begin{align*}
x^{4}+2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.891 |
|
| \begin{align*}
3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.735 |
|
| \begin{align*}
y^{\prime }&=\csc \left (x \right )-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
x^{\prime } t&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.068 |
|
| \begin{align*}
y^{\prime }&=x -3 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
\left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime }&=-2 y x +x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.688 |
|
| \begin{align*}
y^{\prime }&=x -2 y \cot \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.018 |
|
| \begin{align*}
y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.292 |
|
| \begin{align*}
y^{\prime }-m y&=c \,{\mathrm e}^{m x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
2 x \left (y-x^{2}\right )+y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.451 |
|
| \begin{align*}
1+y x -\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.717 |
|
| \begin{align*}
2 y&=\left (x^{2}-1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.292 |
|
| \begin{align*}
\left (1+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.165 |
|
| \begin{align*}
y^{\prime }&=1+3 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.358 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=2 x \left (\left (a^{2}+x^{2}\right )^{2}+3 y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.108 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x -n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.126 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.987 |
|
| \begin{align*}
\left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.932 |
|
| \begin{align*}
y^{\prime }&=x^{3}-2 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.509 |
|
| \begin{align*}
L i^{\prime }+R i&=e \sin \left (w t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| \begin{align*}
y^{\prime }&=4 x -2 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.171 |
|
| \begin{align*}
y^{\prime }&=4 x -2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
\left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\
s \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }&=1-y-\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
\sin \left (\theta \right ) r^{\prime }&=-1-2 r \cos \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| \begin{align*}
1+4 y x -4 x^{2} y+\left (-x^{3}+x^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.590 |
|
| \begin{align*}
3 \left (-1+y\right ) x +y+2+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.640 |
|
| \begin{align*}
y-\sin \left (x \right )^{2}+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.894 |
|
| \begin{align*}
y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.082 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-y \sec \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| \begin{align*}
y^{\prime }&=3 x +y \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.910 |
|
| \begin{align*}
y^{\prime }&=3 x +y \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.141 |
|
| \begin{align*}
x^{2}-1+2 y+\left (-x^{2}+1\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y x -3 x^{2}+2 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.054 |
|
| \begin{align*}
x y^{\prime }-y&=x^{k} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.331 |
|
| \begin{align*}
x y^{\prime }-y&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.753 |
|
| \begin{align*}
x -y+2+3 y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.940 |
|
| \begin{align*}
2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.990 |
|
| \begin{align*}
2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.863 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| \begin{align*}
y^{\prime }&=x -y+2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.973 |
|
| \begin{align*}
x -2 y-1-\left (x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.583 |
|
| \begin{align*}
t y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.128 |
|
| \begin{align*}
y^{\prime }&=2 y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.427 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.821 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.009 |
|
| \begin{align*}
y^{\prime }&=-y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| \begin{align*}
t^{2} y^{\prime }&=1-2 y t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.717 |
|
| \begin{align*}
t y^{\prime }&=y-2 y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.625 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +2 y}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
2 y t +y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.499 |
|
| \begin{align*}
\frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.239 |
|
| \begin{align*}
y t -\left (t +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.262 |
|
| \begin{align*}
3 y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
\cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.942 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.323 |
|
| \begin{align*}
t y^{\prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.758 |
|
| \begin{align*}
t y^{\prime }+m y&=t \ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.923 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| \begin{align*}
y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
t \left (t +1\right ) y^{\prime }&=y+2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.998 |
|
| \begin{align*}
z^{\prime }&=2 t \left (z-t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.658 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t +1}&=\left (t +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.565 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=\frac {t +1}{t} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.403 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.741 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \begin{align*}
y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.520 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| \begin{align*}
t y^{\prime }+2 \ln \left (t \right ) y&=4 \ln \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.407 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \begin{align*}
t y^{\prime }+3 y&=t^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.023 |
|
| \begin{align*}
2 y t +y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t&=1 \\
y \left (2\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
t^{2}-y-t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.399 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.570 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.885 |
|
| \begin{align*}
y^{\prime }&=t -y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| \begin{align*}
t y^{\prime }&=2 y-t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.784 |
|
| \begin{align*}
t y^{\prime }+y&=\ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.153 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.296 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.309 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -2\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.732 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (-4+t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.861 |
|
| \begin{align*}
y+y^{\prime }&=7 \operatorname {Heaviside}\left (-4+t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (-4+t \right )-\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.169 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (-3+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
-y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.282 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| \begin{align*}
y^{\prime }&=-y+\operatorname {Heaviside}\left (-3+t \right )+\delta \left (t -1\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| \begin{align*}
-y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.053 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.079 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.477 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \,{\mathrm e}^{-4 t}+20 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.720 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.114 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.145 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.744 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.530 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\operatorname {Heaviside}\left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.692 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&={\mathrm e}^{c t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.596 |
|
| \begin{align*}
y^{\prime }&=2 y+3 \cos \left (t \right )+4 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
y^{\prime }&=-y-\cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| \begin{align*}
y^{\prime }&=y+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.701 |
|
| \begin{align*}
y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.569 |
|
| \begin{align*}
y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.419 |
|
| \begin{align*}
y^{\prime }&=2 y-{\mathrm e}^{i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.019 |
|
| \begin{align*}
z^{\prime }+4 z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.652 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
48.147 |
|
| \begin{align*}
y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.174 |
|
| \begin{align*}
-2 y+y^{\prime }&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| \begin{align*}
-y+y^{\prime }&=\sin \left (\omega t \right )+\cos \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.021 |
|
| \begin{align*}
y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.524 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.482 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.718 |
|
| \begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| \begin{align*}
y^{\prime }&=y+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.600 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.529 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.022 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.296 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.401 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.191 |
|
| \begin{align*}
y^{\prime }&=y t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.610 |
|
| \begin{align*}
y^{\prime }&=t +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.493 |
|
| \begin{align*}
y^{\prime }&=y t +t +y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.372 |
|
| \begin{align*}
y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.148 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.278 |
|
| \begin{align*}
y^{\prime }&=-4 y t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.008 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }&=4 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.372 |
|
| \begin{align*}
y^{\prime }&=a t y+q \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.839 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} \cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.101 |
|
| \begin{align*}
y^{\prime }-a y&=f \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.131 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{i \omega t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.249 |
|
| \begin{align*}
y^{\prime }-a y&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.134 |
|
| \begin{align*}
y^{\prime }+4 y x&=8 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
x y^{\prime }-3 y x&=1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| \begin{align*}
2 x y^{\prime }-y&=2 x \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.305 |
|
| \begin{align*}
y^{\prime }+2 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.486 |
|
| \begin{align*}
x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.974 |
|
| \begin{align*}
3 x y^{\prime }+5 y&=10 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.391 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.024 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.578 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.826 |
|
| \begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.880 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.731 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.450 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.296 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.597 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.850 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.616 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.174 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.973 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.036 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| \begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.902 |
|
| \begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.704 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.910 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| \begin{align*}
x y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.710 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x \cos \left (x \right )+\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.230 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.753 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.950 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x -3} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.717 |
|
| \begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| \begin{align*}
y^{\prime }+\left (-1+y\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.549 |
|
| \begin{align*}
y+3 x +x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.210 |
|
| \begin{align*}
1-x^{2}+2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.566 |
|
| \begin{align*}
3-2 y+\left (x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.894 |
|
| \begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.060 |
|
| \begin{align*}
2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.089 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.428 |
|
| \begin{align*}
y^{\prime }-2 y&=\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x&=x^{4}+3 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}}-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.422 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{a x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| \begin{align*}
y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.418 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.572 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| \begin{align*}
y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.448 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.570 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.726 |
|
| \begin{align*}
2 y^{\prime }+y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.076 |
|
| \begin{align*}
y&=x y^{\prime }+y^{\prime }-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.705 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.582 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.042 |
|
| \begin{align*}
y^{\prime }-y \cot \left (x \right )&=2 x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&={\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.895 |
|
| \begin{align*}
x y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.361 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.607 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x^{2}+x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
x y^{\prime }&=y+x \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.137 |
|
| \begin{align*}
x y^{\prime }-y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| \begin{align*}
x -y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
y^{\prime }&=y-x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.124 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=x \tan \left (x \right )+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
3 x +y-2+\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| \begin{align*}
2 y+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
\left (x^{2}+2 x -1\right ) y^{\prime }-\left (x +1\right ) y&=x -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.085 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=x^{3} \left (3 \ln \left (x \right )-1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime }+y x&=a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| \begin{align*}
2 x y^{\prime }-y&=3 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.082 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-\left (x +1\right )^{4}-2 y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.720 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
\left (x^{3}+1\right ) x y^{\prime }+\left (2 x^{3}-1\right ) y&=\frac {x^{3}-2}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.137 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (x \right ) \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.515 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y+\frac {\sqrt {x}\, \left (2+\ln \left (x \right )\right )}{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.204 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+y&=x^{2} \left (2 x -1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=\sec \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.415 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{x +1}&={\mathrm e}^{x} \left (x +1\right )^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.526 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=-\frac {\sin \left (x \right )^{2}}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.704 |
|
| \begin{align*}
y^{\prime }-y \,{\mathrm e}^{x}&=\frac {\sin \left (\frac {1}{x}\right )}{x^{2}}-{\mathrm e}^{x} \cos \left (\frac {1}{x}\right ) \\
y \left (-\infty \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.740 |
|
| \begin{align*}
y^{\prime }-y \ln \left (x \right )&=-\left (2 \ln \left (x \right )+1\right ) x^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.850 |
|
| \begin{align*}
\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
30.147 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| \begin{align*}
2 x^{2} y+2 y+5+\left (2 x^{2}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.162 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y&=\sin \left (x \right ) \cos \left (x \right )-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.911 |
|
| \begin{align*}
2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.972 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| \begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )+\frac {18 x -8}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \begin{align*}
x^{\prime }&=t +x \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
x^{\prime }&=2 t \left (t +x\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \begin{align*}
x^{\prime }&=-x+t^{2} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.790 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y+{\mathrm e}^{x}}{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{-x^{2}+2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
x y^{\prime }&=x -y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.671 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (y+2\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.835 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=2 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{-x}}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.053 |
|
| \begin{align*}
2 y+y^{\prime }&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| \begin{align*}
y^{\prime }+y \sec \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.743 |
|
| \begin{align*}
y^{\prime }-2 y&=-8 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| \begin{align*}
y^{\prime }+3 y&=5 \,{\mathrm e}^{2 x}-6 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.575 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=3 x \\
y \left (3\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{4 x} \\
y \left (0\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x +1}&=3 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }+\frac {5 y}{9 x}&=3 x^{3}+x \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.932 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.130 |
|
| \begin{align*}
y^{\prime }&=x \cos \left (2 x \right )-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.852 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right )-3 x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.597 |
|
| \begin{align*}
y^{\prime }&=-y+{\mathrm e}^{x} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right ) y&=-x^{2}+1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.870 |
|
| \begin{align*}
2 y^{\prime }+2 y&=x +3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y-2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }+y&=2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| \begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \begin{align*}
x +2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.593 |
|
| \begin{align*}
x \left (y^{\prime }-y\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.379 |
|
| \begin{align*}
y&=x \left (y^{\prime }-x \cos \left (x \right )\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
y^{\prime }&=2 x \left (x^{2}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \begin{align*}
\left (x y^{\prime }-1\right ) \ln \left (x \right )&=2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=3 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.153 |
|
| \begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
✗ |
14.400 |
|
| \begin{align*}
x^{\prime }+x&=f \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.580 |
|
| \begin{align*}
x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\
x \left (0\right ) &= b \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| \begin{align*}
x y^{\prime }-\left (2 x^{2}+1\right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
x&=\left (x y^{\prime }+y\right ) \sqrt {x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
y^{\prime } \left (2 y-y^{\prime }\right )&=y^{2} \sin \left (x \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \begin{align*}
x \left (-x y^{\prime }+y\right )^{2}&={y^{\prime }}^{2} x -2 y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \begin{align*}
y&=x y^{\prime }-y^{\prime }-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.902 |
|
| \begin{align*}
x y^{\prime }+x^{2}+y x -y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.932 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.305 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x&=3 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.474 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+2 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| \begin{align*}
x \left (x +1\right ) \left (y^{\prime }-1\right )&=y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.631 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| \begin{align*}
3 x^{2}-y&=\sqrt {x^{2}+1}\, y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.797 |
|