| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.572 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.760 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
40.462 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.489 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.734 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.185 |
|
| \begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.264 |
|
| \begin{align*}
y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.158 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.045 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.928 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.276 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.684 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.782 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.489 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.414 |
|
| \begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.505 |
|
| \begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.748 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| \begin{align*}
x y^{\prime }+6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.697 |
|
| \begin{align*}
y^{2} \left (x y^{\prime }+y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.826 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.745 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=3 x^{4}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.685 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.114 |
|
| \begin{align*}
x^{\prime }&=x-x^{2} \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
x^{\prime }&=10 x-x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
x^{\prime }&=4 x \left (7-x\right ) \\
x \left (0\right ) &= 11 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
x^{\prime }&=7 x \left (x-13\right ) \\
x \left (0\right ) &= 17 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.022 |
|
| \begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.076 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.569 |
|
| \begin{align*}
x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.110 |
|
| \begin{align*}
4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.195 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.204 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.162 |
|
| \begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.431 |
|
| \begin{align*}
9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \begin{align*}
3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| \begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.265 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.550 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}-y}{\tan \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.911 |
|
| \begin{align*}
y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.010 |
|
| \begin{align*}
y^{\prime }&=2 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.023 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.299 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
37.945 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.486 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.323 |
|
| \begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.723 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.423 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.484 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.692 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.065 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.797 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.131 |
|
| \begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.618 |
|
| \begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| \begin{align*}
x y^{\prime }+6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.372 |
|
| \begin{align*}
2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.172 |
|
| \begin{align*}
y^{2} \left (x y^{\prime }+y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.941 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.941 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=3 x^{4}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.161 |
|
| \begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.112 |
|
| \begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.881 |
|
| \begin{align*}
x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.314 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.697 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.396 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.032 |
|
| \begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.959 |
|
| \begin{align*}
x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.835 |
|
| \begin{align*}
9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| \begin{align*}
3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| \begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.336 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.222 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.070 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.087 |
|
| \begin{align*}
\sin \left (x \right ) y^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| \begin{align*}
y^{\prime }&=\left (1-2 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{6}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.685 |
|
| \begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.321 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{x} \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y+x^{2} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.348 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \\
y \left (0\right ) &= -\frac {\sqrt {2}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.083 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.916 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.300 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.194 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.683 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.401 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.415 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.247 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.864 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.154 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.540 |
|
| \begin{align*}
y^{\prime }&=y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.312 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.996 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.172 |
|
| \begin{align*}
y^{\prime }&=-b \sqrt {y}+a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.856 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.673 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (y+1\right )}{x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.891 |
|
| \begin{align*}
y^{\prime }&=a y^{\frac {a -1}{a}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.210 |
|
| \begin{align*}
x y^{\prime }+y^{2}+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.396 |
|
| \begin{align*}
y^{\prime }+x \left (y^{2}+y\right )&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
y^{\prime }&=2 x y \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.596 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.565 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
y \left (0\right ) &= \operatorname {y0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.223 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{5}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.977 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.688 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
7 x y^{\prime }-2 y&=-\frac {x^{2}}{y^{6}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
0.375 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\frac {1}{\left (x^{2}+1\right ) y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
y^{\prime }-y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
y^{\prime }-\frac {\left (x +1\right ) y}{3 x}&=y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime }-2 y&=x y^{3} \\
y \left (0\right ) &= 2 \sqrt {2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
y^{\prime }-y x&=x y^{{3}/{2}} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.500 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} y^{4} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }-2 y&=2 \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.046 |
|
| \begin{align*}
y^{\prime }-4 y&=\frac {48 x}{y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{3} \\
y \left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
y^{\prime }-y&=x \sqrt {y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
1.049 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.181 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}+x^{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
98.177 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.547 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.059 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.503 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.773 |
|
| \begin{align*}
x y y^{\prime }&=3 x^{2}+4 y^{2} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.819 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=y^{3}+x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
x y y^{\prime }&=3 x^{6}+6 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.185 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.759 |
|
| \begin{align*}
\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.284 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{2} x^{4}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.239 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.531 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.642 |
|
| \begin{align*}
3 x^{2} y^{2}+2 y+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.267 |
|
| \begin{align*}
t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.428 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t}{y+t^{2} y} \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.079 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.074 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.100 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.773 |
|
| \begin{align*}
t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.688 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t}{y+t^{2} y} \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.178 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.696 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.923 |
|
| \begin{align*}
y^{\prime }&=t y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
139.743 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.994 |
|
| \begin{align*}
y^{\prime }&=t y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.126 |
|
| \begin{align*}
x^{\prime }&=x \left (1-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
x^{\prime }&=-x \left (1-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.943 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \begin{align*}
x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.939 |
|
| \begin{align*}
x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.331 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.834 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.598 |
|
| \begin{align*}
y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.615 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.194 |
|
| \begin{align*}
\left (x^{2}+3 x \right ) y^{\prime }&=y^{3}+2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
17.432 |
|
| \begin{align*}
x^{2}+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.587 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.293 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.952 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.695 |
|
| \begin{align*}
y \left (y-x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.053 |
|
| \begin{align*}
{\mathrm e}^{x} y^{\prime }&=2 x y^{2}+y \,{\mathrm e}^{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+{\mathrm e}^{x} x^{4}-2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.457 |
|
| \begin{align*}
y \left (1-y^{2} x^{4}\right )+x y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.577 |
|
| \begin{align*}
3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.775 |
|
| \begin{align*}
y^{3} y^{\prime }+x y^{4}&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.052 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.618 |
|
| \begin{align*}
y^{\prime }-y x&=\sqrt {y}\, x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.951 |
|
| \begin{align*}
x^{\prime } t +x \left (1-x^{2} t^{4}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.599 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.720 |
|
| \begin{align*}
y^{\prime }-y x&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.454 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} x^{2} \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.316 |
|
| \begin{align*}
r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.775 |
|
| \begin{align*}
x y^{\prime }+2 y&=3 x^{3} y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.083 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x}{y^{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.326 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.909 |
|
| \begin{align*}
y+y^{\prime }&=y^{2} {\mathrm e}^{-t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.850 |
|
| \begin{align*}
-x y^{\prime }+y&=2 y^{\prime }+2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| \begin{align*}
3 x -6&=x y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| \begin{align*}
2 x y^{\prime }-y+\frac {x^{2}}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.303 |
|
| \begin{align*}
x y^{\prime }+y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.205 |
|
| \begin{align*}
x y^{\prime }-5 y-x \sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.000 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.780 |
|
| \begin{align*}
x y^{\prime }-2 y-2 x^{4} y^{3}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.147 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} y^{6} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.540 |
|
| \begin{align*}
x^{\prime }&=x+x^{2} {\mathrm e}^{\theta } \\
x \left (0\right ) &= 2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.503 |
|
| \begin{align*}
4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.709 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.747 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.214 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.155 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\
y \left (\ln \left (2\right )\right ) &= -8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.750 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.801 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.709 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| \begin{align*}
x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.262 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.860 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.170 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.285 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \\
y \left (\pi \right ) &= \frac {1}{\pi } \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.490 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.473 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| \begin{align*}
y^{\prime }+\frac {y \tan \left (x \right )}{2}&=2 y^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.079 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.904 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.477 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.078 |
|
| \begin{align*}
2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.237 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.646 |
|
| \begin{align*}
y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.441 |
|
| \begin{align*}
y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.072 |
|
| \begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.118 |
|
| \begin{align*}
2 y^{\prime }+y \cot \left (x \right )&=\frac {8 \cos \left (x \right )^{3}}{y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.720 |
|
| \begin{align*}
\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )&=y^{\sqrt {3}} \sec \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.967 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=y^{3} \sin \left (x \right )^{3} \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.139 |
|
| \begin{align*}
x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.465 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-x^{2} y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.917 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.827 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=2 x -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.202 |
|
| \begin{align*}
y^{\prime }&=6 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.284 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.166 |
|
| \begin{align*}
x y^{\prime }&=2 y \left (-1+y\right ) \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.881 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x} y^{\prime }+2 x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.954 |
|
| \begin{align*}
x y y^{\prime }&=2 x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.926 |
|
| \begin{align*}
x^{2}-y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.314 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.348 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.273 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.395 |
|
| \begin{align*}
2+y^{2}+2 x +2 y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.487 |
|
| \begin{align*}
1-\left (y-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.692 |
|
| \begin{align*}
3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.235 |
|
| \begin{align*}
\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x y y^{\prime }+y^{2}-\sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.113 |
|
| \begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.072 |
|
| \begin{align*}
{\mathrm e}^{x}+3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.724 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.234 |
|
| \begin{align*}
x^{2} \left (x y^{\prime }-y\right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.810 |
|
| \begin{align*}
2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.072 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.297 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.378 |
|
| \begin{align*}
y^{\prime }&=x y \left (y+3\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.349 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.109 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.178 |
|
| \begin{align*}
y^{\prime }&=y \left (a +b y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.643 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.282 |
|
| \begin{align*}
y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.262 |
|
| \begin{align*}
y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.759 |
|
| \begin{align*}
y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.144 |
|
| \begin{align*}
y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| \begin{align*}
y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.677 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.759 |
|
| \begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
x y^{\prime }+\left (-y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.570 |
|
| \begin{align*}
x y^{\prime }&=\left (-y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.580 |
|
| \begin{align*}
x y^{\prime }&=\left (y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.031 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{3} \left (-y x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.776 |
|
| \begin{align*}
x y^{\prime }+\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.353 |
|
| \begin{align*}
x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.358 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.938 |
|
| \begin{align*}
x y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.365 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.107 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
x y^{\prime }&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.597 |
|
| \begin{align*}
x y^{\prime }&=a y+b \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.555 |
|
| \begin{align*}
x y^{\prime }+2 y&=a \,x^{2 k} y^{k} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.773 |
|
| \begin{align*}
x y^{\prime }&=4 y-4 \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.864 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.807 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.876 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.314 |
|
| \begin{align*}
\left (-x +a \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.770 |
|
| \begin{align*}
2 x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.481 |
|
| \begin{align*}
2 x y^{\prime }+y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.595 |
|
| \begin{align*}
2 x y^{\prime }&=\left (1+x -6 y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.276 |
|
| \begin{align*}
2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.051 |
|
| \begin{align*}
3 x y^{\prime }&=\left (2+x y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.257 |
|
| \begin{align*}
3 x y^{\prime }&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.857 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (x +a y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.296 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.834 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.733 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.107 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.326 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.783 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.349 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.882 |
|
| \begin{align*}
\left (-x^{2}+4\right ) y^{\prime }+4 y&=\left (x +2\right ) y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.584 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.575 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.516 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.717 |
|
| \begin{align*}
x \left (x +a \right ) y^{\prime }&=\left (b +c y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.095 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.520 |
|
| \begin{align*}
x^{3} y^{\prime }&=y \left (x^{2}+y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.696 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.291 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
76.477 |
|
| \begin{align*}
x^{2} \left (1-x \right ) y^{\prime }&=x \left (2-x \right ) y-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.618 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.664 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.688 |
|
| \begin{align*}
6 x^{3} y^{\prime }&=4 x^{2} y+\left (-3 x +1\right ) y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.865 |
|
| \begin{align*}
x^{4} y^{\prime }&=\left (y+x^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.669 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.541 |
|
| \begin{align*}
y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )&=y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.064 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.704 |
|
| \begin{align*}
y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.283 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.451 |
|
| \begin{align*}
y y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.895 |
|
| \begin{align*}
y y^{\prime }&=b \cos \left (x +c \right )+a y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.037 |
|
| \begin{align*}
y y^{\prime }&=a x +b x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.683 |
|
| \begin{align*}
y y^{\prime }&=\csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.382 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.164 |
|
| \begin{align*}
2 y y^{\prime }&=x y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.709 |
|
| \begin{align*}
x y y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.530 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.833 |
|
| \begin{align*}
x y y^{\prime }+x^{4}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.169 |
|
| \begin{align*}
x y y^{\prime }&=a \,x^{3} \cos \left (x \right )+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.753 |
|
| \begin{align*}
x y y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.694 |
|
| \begin{align*}
x y y^{\prime }&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
14.744 |
|
| \begin{align*}
x y y^{\prime }&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.428 |
|
| \begin{align*}
2 x y y^{\prime }+1-2 x^{3}-y^{2}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.927 |
|
| \begin{align*}
2 x y y^{\prime }+a +y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.499 |
|
| \begin{align*}
2 x y y^{\prime }&=a x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.408 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.964 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.068 |
|
| \begin{align*}
2 x y y^{\prime }&=4 x^{2} \left (2 x +1\right )+y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.647 |
|
| \begin{align*}
2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right )&=6 y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.006 |
|
| \begin{align*}
2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2}&=0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.379 |
|
| \begin{align*}
a x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.247 |
|
| \begin{align*}
a x y y^{\prime }+x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.010 |
|
| \begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.641 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.590 |
|
| \begin{align*}
2 x^{2} y y^{\prime }&=x^{2} \left (2 x +1\right )-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.431 |
|
| \begin{align*}
2 \left (x +1\right ) x y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.227 |
|
| \begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.845 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+a +3 x^{2} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.646 |
|
| \begin{align*}
x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.490 |
|
| \begin{align*}
3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.707 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=1+x +a y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.503 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=2 x -y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.994 |
|
| \begin{align*}
6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| \begin{align*}
x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.012 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.273 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.944 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.625 |
|
| \begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.214 |
|
| \begin{align*}
3 z^{2} z^{\prime }-a z^{3}&=x +1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.362 |
|
| \begin{align*}
z^{\prime }+2 x z&=2 a \,x^{3} z^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.305 |
|
| \begin{align*}
z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.222 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.351 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
124.164 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
74.717 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.686 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.763 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.138 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.484 |
|
| \begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.345 |
|
| \begin{align*}
x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.606 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
112.611 |
|
| \begin{align*}
2 \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )-y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.734 |
|
| \begin{align*}
2 x y y^{\prime }+\left (x +1\right ) y^{2}&={\mathrm e}^{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.315 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.592 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.357 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| \begin{align*}
2 x y y^{\prime }+3 x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.243 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.097 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.605 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.915 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.688 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\
y \left (\sqrt {2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.595 |
|
| \begin{align*}
y y^{\prime }+x y^{2}-8 x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
y^{\prime }+y&=x y^{{2}/{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.891 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+3 y^{3}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.033 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.275 |
|
| \begin{align*}
y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.764 |
|
| \begin{align*}
y^{\prime }+y x&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.575 |
|
| \begin{align*}
\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.183 |
|
| \begin{align*}
x y^{\prime }&=\frac {1}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.695 |
|
| \begin{align*}
x^{\prime }-x^{3}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.873 |
|
| \begin{align*}
x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.334 |
|
| \begin{align*}
\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.526 |
|
| \begin{align*}
x^{2}+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.228 |
|
| \begin{align*}
\sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.421 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.664 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.587 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
47.765 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.235 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.434 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.641 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.691 |
|
| \begin{align*}
2 y+y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.532 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.973 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.513 |
|
| \begin{align*}
2 t x x^{\prime }+t^{2}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.142 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.155 |
|
| \begin{align*}
y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.808 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.288 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.838 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.846 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.407 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.967 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.698 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
r^{\prime }&=r^{2}+\frac {2 r}{t} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.793 |
|
| \begin{align*}
y^{\prime }+x y^{3}+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.164 |
|
| \begin{align*}
2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.957 |
|
| \begin{align*}
t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.658 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=2 x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.957 |
|
| \begin{align*}
x^{2}+y^{2}+3 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.281 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.864 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (1\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.488 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| \begin{align*}
\sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.286 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.260 |
|
| \begin{align*}
y^{\prime }-4 y&=2 x y^{2} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| \begin{align*}
y^{\prime }&=2 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.714 |
|
| \begin{align*}
3 x y^{\prime }+y+x^{2} y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.567 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.618 |
|
| \begin{align*}
x y^{\prime }+3 y&=x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.151 |
|
| \begin{align*}
x^{3}+y^{3}&=3 x y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.731 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
y^{\prime }-2 y \tan \left (x \right )&=y^{2} \tan \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=y^{3} \sec \left (x \right )^{4} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime }-y \cot \left (x \right )&=y^{2} \sec \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.213 |
|
| \begin{align*}
x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.634 |
|
| \begin{align*}
\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\
r \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.780 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.390 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.371 |
|
| \begin{align*}
y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.429 |
|
| \begin{align*}
y^{2}-x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.808 |
|
| \begin{align*}
x^{3}+y^{3}+3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.563 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.503 |
|
| \begin{align*}
y^{2}+y x -x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.295 |
|
| \begin{align*}
y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.983 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.303 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.366 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.209 |
|
| \begin{align*}
x y^{\prime }+y-x^{3} y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.421 |
|
| \begin{align*}
y y^{\prime }-x y^{2}+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.335 |
|
| \begin{align*}
2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.685 |
|
| \begin{align*}
2 y^{5} x -y+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.902 |
|
| \begin{align*}
x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.766 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.560 |
|
| \begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.395 |
|
| \begin{align*}
p^{\prime }&=p \left (1-p\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.929 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.448 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.856 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.680 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.339 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.128 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.925 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.251 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.576 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.359 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.086 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.181 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.594 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.375 |
|
| \begin{align*}
y^{\prime }&=y \left (-3+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.584 |
|
| \begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.951 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.392 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.060 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.155 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.387 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.885 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.247 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.404 |
|
| \begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.542 |
|
| \begin{align*}
p^{\prime }&=p-p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.083 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.831 |
|
| \begin{align*}
y^{\prime }&=y^{2} \sin \left (x^{2}\right ) \\
y \left (-2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.533 |
|
| \begin{align*}
y^{\prime }&=\frac {1+3 x}{2 y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.496 |
|
| \begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.238 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.670 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
14.598 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.046 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.257 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.344 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.109 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.997 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.792 |
|
| \begin{align*}
y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.541 |
|
| \begin{align*}
\left (\sqrt {x}+x \right ) y^{\prime }&=\sqrt {y}+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.549 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
54.648 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.534 |
|
| \begin{align*}
y^{\prime }&=\frac {x \arctan \left (x \right )}{y} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.043 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.575 |
|
| \begin{align*}
m^{\prime }&=-\frac {k}{m^{2}} \\
m \left (0\right ) &= m_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
6.267 |
|
| \begin{align*}
y y^{\prime }-x&=2 y^{2} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.756 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.638 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.004 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.321 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.943 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.037 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| \begin{align*}
{\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.725 |
|
| \begin{align*}
\frac {y}{x -1}+\frac {x y^{\prime }}{y+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| \begin{align*}
\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.169 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.947 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.479 |
|
| \begin{align*}
2 x y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.306 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.842 |
|
| \begin{align*}
2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.553 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.833 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.863 |
|
| \begin{align*}
\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.250 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.046 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.087 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.756 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.497 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.609 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.164 |
|
| \begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.972 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.533 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.411 |
|
| \begin{align*}
x y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.806 |
|
| \begin{align*}
y y^{\prime }&=x +1 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.135 |
|
| \begin{align*}
\frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.820 |
|
| \begin{align*}
y^{2} y^{\prime }&=x +2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.277 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.135 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.801 |
|
| \begin{align*}
x y^{2} y^{\prime }+y^{3}&=x \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.408 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.635 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.129 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.487 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.155 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.839 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.747 |
|
| \begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.514 |
|
| \begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.405 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \\
y \left (-1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.951 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.122 |
|
| \begin{align*}
y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
y^{2}+\frac {2}{x}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.474 |
|
| \begin{align*}
f^{\prime }&=\frac {1}{f} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.298 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.803 |
|
| \begin{align*}
y^{\prime }&=2 y \left (x \sqrt {y}-1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| \begin{align*}
v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.927 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.965 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
53.574 |
|
| \begin{align*}
y^{\prime }-x y^{2}-3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.406 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.149 |
|
| \begin{align*}
y^{\prime }+2 a \,x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.595 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.471 |
|
| \begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.630 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| \begin{align*}
3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.656 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.287 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.523 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.359 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.707 |
|
| \begin{align*}
x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.381 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.074 |
|
| \begin{align*}
y y^{\prime }+a y^{2}-b \cos \left (x +c \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.083 |
|
| \begin{align*}
y y^{\prime }+x y^{2}-4 x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.544 |
|
| \begin{align*}
2 y y^{\prime }-x y^{2}-x^{3}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.001 |
|
| \begin{align*}
a y y^{\prime }+b y^{2}+f \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.289 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.393 |
|
| \begin{align*}
x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.665 |
|
| \begin{align*}
2 x y y^{\prime }-y^{2}+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.938 |
|
| \begin{align*}
2 x y y^{\prime }-y^{2}+a \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.817 |
|
| \begin{align*}
2 x y y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.844 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.758 |
|
| \begin{align*}
2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.655 |
|
| \begin{align*}
y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.178 |
|
| \begin{align*}
f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.360 |
|
| \begin{align*}
6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.272 |
|
| \begin{align*}
x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.181 |
|
| \begin{align*}
x \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.004 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.542 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1-x +y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
6.798 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
8.748 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.140 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.506 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.385 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
8.126 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.605 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.166 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.220 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.985 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
14.178 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.449 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.422 |
|
| \begin{align*}
g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.306 |
|
| \begin{align*}
\left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.024 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.502 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
77.725 |
|
| \begin{align*}
y^{3}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.206 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
5.220 |
|
| \begin{align*}
y y^{\prime }+x y^{2}&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.770 |
|
| \begin{align*}
4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.156 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.736 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.553 |
|
| \begin{align*}
x y^{\prime }+y+{\mathrm e}^{x} x^{4} y^{4}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.623 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.158 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.417 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.599 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.992 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.506 |
|
| \begin{align*}
x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.046 |
|
| \begin{align*}
y^{\prime }+y+\frac {1}{y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.524 |
|
| \begin{align*}
\left (t +1\right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.839 |
|
| \begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.350 |
|
| \begin{align*}
x^{\prime }&=x \left (4+x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.325 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.769 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.826 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y t}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.196 |
|
| \begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.388 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
68.100 |
|
| \begin{align*}
x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.092 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.992 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.270 |
|
| \begin{align*}
x^{\prime }&=a x+b x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.169 |
|
| \begin{align*}
w^{\prime }&=t w+t^{3} w^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.393 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.280 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.989 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.360 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x -2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.105 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
75.683 |
|
| \begin{align*}
4 x +3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.530 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.958 |
|
| \begin{align*}
\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.565 |
|
| \begin{align*}
\left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
8.581 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\
y \left (2\right ) &= 6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.297 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| \begin{align*}
x y^{\prime }+y&=-2 x^{6} y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.737 |
|
| \begin{align*}
y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.237 |
|
| \begin{align*}
x^{\prime }+\frac {\left (t +1\right ) x}{2 t}&=\frac {t +1}{x t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.355 |
|
| \begin{align*}
y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.752 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.299 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.500 |
|
| \begin{align*}
8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
10.054 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.650 |
|
| \begin{align*}
4 x y y^{\prime }&=1+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.404 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
204.229 |
|
| \begin{align*}
x^{\prime }&=x \left (2-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.461 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.676 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.172 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.428 |
|
| \begin{align*}
x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✗ |
183.655 |
|
| \begin{align*}
V^{\prime }\left (x \right )+2 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.759 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.918 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
39.815 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x +1}+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.363 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.768 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t}+\frac {x^{2}}{t^{3}} \\
x \left (2\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.259 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.174 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.015 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.608 |
|
| \begin{align*}
3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.098 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.033 |
|
| \begin{align*}
y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.318 |
|
| \begin{align*}
x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.107 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.640 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.189 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.723 |
|
| \begin{align*}
3 y^{2} y^{\prime }-a y^{3}-x -1&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.197 |
|
| \begin{align*}
x y^{\prime }&=\left (y \ln \left (x \right )-2\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.195 |
|
| \begin{align*}
y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.599 |
|
| \begin{align*}
\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.918 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.929 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.068 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.304 |
|
| \begin{align*}
y^{\prime }+\frac {1}{2 y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.382 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.897 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.445 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.439 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.466 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.672 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x}+y^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
46.973 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
85.439 |
|
| \begin{align*}
y^{\prime }&=y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
4.849 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \begin{align*}
2 x y y^{\prime }+y^{2}&=-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.841 |
|
| \begin{align*}
x -y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.604 |
|
| \begin{align*}
x y \left (1-y\right )-2 y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
14.324 |
|
| \begin{align*}
x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
36.377 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
20.183 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.992 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
20.897 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
36.233 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.490 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
49.432 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.570 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.170 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
48.282 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
16.067 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.271 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.366 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.710 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
43.302 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
83.362 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
32.628 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.229 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
89.987 |
|
| \begin{align*}
y^{\prime }&=y^{2} t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.696 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.223 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y+t^{2} y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| \begin{align*}
y^{\prime }&=t y^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.281 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.678 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.343 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y-t^{2} y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.639 |
|
| \begin{align*}
y^{\prime }&=t y^{2}+2 y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.564 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\
x \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.797 |
|
| \begin{align*}
y^{\prime }&=\frac {1-y^{2}}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.156 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
y^{\prime }&=3 y \left (1-y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.267 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.192 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
y^{\prime }&=y t +t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.806 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.131 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.336 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.544 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.698 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.586 |
|
| \begin{align*}
y^{\prime }&=3 y \left (-2+y\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.853 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3}+y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.355 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| \begin{align*}
y y^{\prime }&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.122 |
|
| \begin{align*}
y^{3}-25 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.260 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.251 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.627 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.156 |
|
| \begin{align*}
x y y^{\prime }&=y^{2}+9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.000 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.335 |
|
| \begin{align*}
y y^{\prime }&=x y^{2}+x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.137 |
|
| \begin{align*}
y y^{\prime }&=x y^{2}-9 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.463 |
|
| \begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.648 |
|
| \begin{align*}
y^{\prime }&=3 x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.119 |
|
| \begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
y y^{\prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.109 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.799 |
|
| \begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
5.263 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-1}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.401 |
|
| \begin{align*}
y^{\prime }+4 y&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.878 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.974 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.340 |
|
| \begin{align*}
y^{\prime }+3 y&=3 y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.657 |
|
| \begin{align*}
y^{\prime }+3 y \cot \left (x \right )&=6 \cos \left (x \right ) y^{{2}/{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.386 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.469 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.084 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.889 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| \begin{align*}
y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y}-\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.864 |
|
| \begin{align*}
2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.744 |
|
| \begin{align*}
2-2 x +3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.331 |
|
| \begin{align*}
1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| \begin{align*}
1+y^{4}+x y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.201 |
|
| \begin{align*}
x y^{\prime }&=2 y^{2}-6 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.275 |
|
| \begin{align*}
4 y^{2}-x^{2} y^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.467 |
|
| \begin{align*}
x y^{2}-6+x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.139 |
|
| \begin{align*}
x^{3}+y^{3}+x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.812 |
|
| \begin{align*}
1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.341 |
|
| \begin{align*}
3 x y^{3}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.349 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{x +1}-y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.390 |
|
| \begin{align*}
x y y^{\prime }&=2 x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.858 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.115 |
|
| \begin{align*}
y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.711 |
|
| \begin{align*}
y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.927 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.627 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.132 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.597 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{5}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
48.957 |
|
| \begin{align*}
\frac {y^{\prime }}{t}&=\sqrt {y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
35.115 |
|
| \begin{align*}
y^{\prime }&=6 y^{{2}/{3}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.917 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.189 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.471 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
41.807 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.314 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.146 |
|
| \begin{align*}
\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.683 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.724 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| \begin{align*}
y^{\prime }&=\frac {5^{-t}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.138 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.431 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.052 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {t}}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.276 |
|
| \begin{align*}
y^{\prime }&=y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.796 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.536 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
y^{\prime }&=16 y-8 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.520 |
|
| \begin{align*}
\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.264 |
|
| \begin{align*}
-1+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.535 |
|
| \begin{align*}
2 y t +y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.727 |
|
| \begin{align*}
5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.412 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.517 |
|
| \begin{align*}
y+y^{\prime }&=t y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.033 |
|
| \begin{align*}
2 t y^{\prime }-y&=2 t y^{3} \cos \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.837 |
|
| \begin{align*}
-y+t y^{\prime }&=t y^{3} \sin \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.722 |
|
| \begin{align*}
-2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.002 |
|
| \begin{align*}
3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.285 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.863 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.779 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.812 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t^{2} y^{{3}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.812 |
|
| \begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.784 |
|
| \begin{align*}
\sqrt {t^{2}+1}+y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.542 |
|
| \begin{align*}
t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.119 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
3.932 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
3.908 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 y t} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.437 |
|
| \begin{align*}
y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.387 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
8.859 |
|
| \begin{align*}
y^{\prime }&=\frac {-t^{2}+y^{2}}{y t} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.763 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.786 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.450 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.225 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.959 |
|
| \begin{align*}
-y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.957 |
|
| \begin{align*}
y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| \begin{align*}
y-t y^{\prime }&=2 y^{2} \ln \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.825 |
|
| \begin{align*}
y^{\prime }&=t y^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
26.632 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y^{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
35.856 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.878 |
|
| \begin{align*}
y^{\prime }&=y+3 y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.635 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.761 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.597 |
|
| \begin{align*}
4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.277 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.554 |
|
| \begin{align*}
3 x y^{2} y^{\prime }-2 y^{3}&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.244 |
|
| \begin{align*}
2 \ln \left (x \right ) y^{\prime }+\frac {y}{x}&=\frac {\cos \left (x \right )}{y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.462 |
|
| \begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.341 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.482 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.351 |
|
| \begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.593 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.608 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.474 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.708 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.829 |
|
| \begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.727 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.543 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.221 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.851 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.762 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.543 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.591 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.454 |
|
| \begin{align*}
y^{\prime }+y^{3} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.986 |
|
| \begin{align*}
y y^{\prime }&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.743 |
|
| \begin{align*}
y^{\prime }&=x \left (y-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.852 |
|
| \begin{align*}
y^{\prime }&=\left (1-12 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{8}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.377 |
|
| \begin{align*}
y^{\prime }&=\frac {3-2 x}{y} \\
y \left (1\right ) &= -6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.894 |
|
| \begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.227 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{\theta } \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.868 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x}{y+x^{2} y} \\
y \left (0\right ) &= -7 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.995 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.955 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\
y \left (0\right ) &= -2^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.940 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-4}} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.989 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.842 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
10.971 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
14.471 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
77.033 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
21.904 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.780 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.333 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
5.789 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.116 |
|
| \begin{align*}
y^{\prime }&=y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.870 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-y t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.632 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.427 |
|
| \begin{align*}
y y^{\prime }&=x +1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.912 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }&=y \left (y+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.375 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.776 |
|
| \begin{align*}
t y^{\prime }+y&=y^{2} t^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.494 |
|
| \begin{align*}
y^{\prime }&=y \left (t y^{3}-1\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.304 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{t}&=y^{2} t^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| \begin{align*}
t^{2} y^{\prime }+2 y t -y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.563 |
|
| \begin{align*}
3 t y^{\prime }+9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.161 |
|
| \begin{align*}
y^{\prime }&=y+\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.015 |
|
| \begin{align*}
y^{\prime }&=r y-k^{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.880 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.325 |
|
| \begin{align*}
y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.176 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.568 |
|
| \begin{align*}
2 x y y^{\prime }+\ln \left (x \right )&=-1-y^{2} \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.530 |
|
| \begin{align*}
4 x y y^{\prime }&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.504 |
|
| \begin{align*}
y^{\prime }+y-y^{{1}/{4}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.157 |
|
| \begin{align*}
x y^{\prime }-4 y&=x^{2} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.902 |
|
| \begin{align*}
y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.596 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.317 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.793 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.709 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.980 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.444 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.664 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.889 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.430 |
|
| \begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.673 |
|
| \begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.207 |
|
| \begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.747 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.393 |
|
| \begin{align*}
x +3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.341 |
|
| \begin{align*}
x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.525 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.886 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.605 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.591 |
|
| \begin{align*}
x y^{2} y^{\prime }+y^{3}&=x \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.433 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.828 |
|
| \begin{align*}
x y^{\prime }+y&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.831 |
|
| \begin{align*}
x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
98.308 |
|
| \begin{align*}
x y^{2}+y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.876 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.697 |
|
| \begin{align*}
x^{\prime }&=2 \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.029 |
|
| \begin{align*}
x^{\prime }+2 x t +t x^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
78.055 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {\sin \left (x \right )}{y^{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.605 |
|
| \begin{align*}
\left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.183 |
|
| \begin{align*}
y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.943 |
|
| \begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.285 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.441 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.297 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.959 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&=x -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=y^{4} \sec \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.517 |
|
| \begin{align*}
5 x y y^{\prime }-x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.125 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.586 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.672 |
|
| \begin{align*}
{\mathrm e}^{x} x^{4}-2 m x y^{2}+2 m \,x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.073 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.250 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.616 |
|
| \begin{align*}
x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.528 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.259 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=3 x^{2} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.689 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.182 |
|
| \begin{align*}
3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=a \,x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.534 |
|
| \begin{align*}
x y^{\prime }+\frac {y^{2}}{x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.112 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.125 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.151 |
|
| \begin{align*}
y^{\prime }&=x^{3} y^{3}-y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| \begin{align*}
y y^{\prime }&=a x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.958 |
|
| \begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.645 |
|
| \begin{align*}
x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.485 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.427 |
|
| \begin{align*}
\left (y x +1\right ) y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.723 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.563 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.079 |
|
| \begin{align*}
x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.801 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.983 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.635 |
|
| \begin{align*}
x^{2} y^{\prime }+y \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \begin{align*}
2 y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.786 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.559 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.493 |
|
| \begin{align*}
2 y^{\prime }-y \sec \left (x \right )&=y^{3} \tan \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.319 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.120 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.232 |
|
| \begin{align*}
y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 x y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.383 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.855 |
|
| \begin{align*}
x^{2} y^{2}-3 x y y^{\prime }&=2 y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
4.087 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.903 |
|
| \begin{align*}
1+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.916 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.175 |
|
| \begin{align*}
x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.948 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.166 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.740 |
|
| \begin{align*}
x y^{\prime }&=y \left (-2 y+1\right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.117 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.487 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.329 |
|
| \begin{align*}
y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.146 |
|
| \begin{align*}
y^{\prime }&=k y-c y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.830 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.500 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.124 |
|
| \begin{align*}
y^{\prime }&=y-\mu y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.432 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.264 |
|
| \begin{align*}
\left (y x +1\right ) y&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.911 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{{1}/{3}}}{2} \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.973 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
x \left (t_{0} \right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.074 |
|
| \begin{align*}
x^{\prime }&=x^{{1}/{4}} \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.329 |
|
| \begin{align*}
x^{\prime }&=x^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.151 |
|
| \begin{align*}
x^{\prime }&=x^{3}-x \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.207 |
|
| \begin{align*}
x^{\prime }&=x^{2}+x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.531 |
|
| \begin{align*}
x^{\prime }&=4 t^{3} x^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.135 |
|
| \begin{align*}
x^{\prime }&=-t x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.230 |
|
| \begin{align*}
x^{\prime }&=\frac {t}{x} \\
x \left (\sqrt {2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.966 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{4 x^{3}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.780 |
|
| \begin{align*}
x^{\prime }&=-t^{2} x^{2} \\
x \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.530 |
|
| \begin{align*}
x^{\prime }&=5 t \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
20.065 |
|
| \begin{align*}
x^{\prime }&=4 t^{3} \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
20.529 |
|
| \begin{align*}
x^{\prime }&=2 t \sqrt {x} \\
x \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.448 |
|
| \begin{align*}
x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.784 |
|
| \begin{align*}
x -2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.950 |
|
| \begin{align*}
x +y^{2}+B \left (x \right ) y y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.437 |
|
| \begin{align*}
x +y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.743 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.589 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.326 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}+x^{2}}{2 x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.088 |
|
| \begin{align*}
x^{\prime }-x&=t x^{2} \\
x \left (0\right ) &= a \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.310 |
|
| \begin{align*}
x^{\prime }+2 x t&=-4 t x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.328 |
|
| \begin{align*}
x^{\prime }-x t&=x^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| \begin{align*}
x^{\prime }&=\lambda x-x^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.292 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.963 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.774 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (0\right ) &= a_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
11.514 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.296 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.904 |
|
| \begin{align*}
x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.492 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.948 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.323 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
60.649 |
|
| \begin{align*}
y^{2}-x^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.719 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.529 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
105.995 |
|
| \begin{align*}
2 x y y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.270 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
99.834 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.792 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.643 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
17.003 |
|
| \begin{align*}
y-x y^{2}+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.128 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.599 |
|
| \begin{align*}
\frac {y^{2}-y x}{x y^{2}}+\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.280 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y^{2}+2 y}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.755 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.414 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.125 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.454 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.438 |
|
| \begin{align*}
y^{\prime }&=\alpha \left (A -y\right ) y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.689 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.487 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.782 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.915 |
|
| \begin{align*}
3 x^{2}-2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.895 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.566 |
|
| \begin{align*}
x^{3}-y^{3}+x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.930 |
|
| \begin{align*}
x y \left (x y^{\prime }+y\right )&=4 x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.104 |
|
| \begin{align*}
y y^{\prime }+\tan \left (x \right ) y^{2}&=\cos \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.576 |
|
| \begin{align*}
x y^{\prime }-y&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.526 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} x^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.526 |
|
| \begin{align*}
x y^{2}&=-x y^{\prime }+y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.069 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.209 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.119 |
|
| \begin{align*}
\sin \left (x \right )+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.453 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.181 |
|
| \begin{align*}
x -y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.061 |
|
| \begin{align*}
y^{\prime }&=x^{3} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.472 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.832 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| \begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.247 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.573 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
106.064 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.612 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 x}{y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.525 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.925 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.576 |
|
| \begin{align*}
y^{\prime }&=\frac {-y+x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
y+x^{3} y^{3}+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.543 |
|
| \begin{align*}
y+y^{2} x^{4}+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.424 |
|
| \begin{align*}
1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.983 |
|
| \begin{align*}
2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.912 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.085 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.013 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
y^{\prime }+y x&=6 x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.457 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.706 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.164 |
|
| \begin{align*}
y^{\prime }&=y^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.644 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.452 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.495 |
|
| \begin{align*}
3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.542 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}+x}{4 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.670 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.667 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.757 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.042 |
|
| \begin{align*}
x^{2}-y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.269 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.598 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.470 |
|
| \begin{align*}
2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.563 |
|
| \begin{align*}
3 x +4 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.371 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.336 |
|
| \begin{align*}
y^{2}+2 x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.763 |
|
| \begin{align*}
3 x +2 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.781 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2} \cot \left (x \right )+\sin \left (x \right ) \cos \left (x \right )}{2 y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.474 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.062 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.281 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.769 |
|
| \begin{align*}
\left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.889 |
|
| \begin{align*}
s^{2} t s^{\prime }+t^{2}+4&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.330 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.408 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x -y^{4}}{3 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.917 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.194 |
|
| \begin{align*}
3 x y^{2}+2+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.705 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.041 |
|
| \begin{align*}
y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✗ |
✓ |
6.290 |
|
| \begin{align*}
y^{2}+x y y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.502 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y^{2}}{2 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.223 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.440 |
|
| \begin{align*}
y y^{\prime }&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.799 |
|
| \begin{align*}
x y^{\prime }&=\left (x +1\right ) y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.296 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.758 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.235 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.312 |
|
| \begin{align*}
r r^{\prime }&=a \\
r \left (0\right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
1.034 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.323 |
|
| \begin{align*}
y y^{\prime }-y^{2}&=x^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.955 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.977 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.395 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.575 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.754 |
|
| \begin{align*}
x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
108.157 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
x y^{\prime }-\frac {y}{\ln \left (x \right )}&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.671 |
|
| \begin{align*}
\left (1+y^{2}\right ) \cos \left (x \right )&=2 \left (1+\sin \left (x \right )^{2}\right ) y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.415 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.411 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.086 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
y^{\prime }-2 y x&=4 x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
x y^{\prime }-\frac {y}{2 \ln \left (x \right )}&=y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.451 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.603 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.957 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.352 |
|
| \begin{align*}
x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
96.533 |
|
| \begin{align*}
x^{2}-y^{2}+x +2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.469 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.560 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.425 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.413 |
|
| \begin{align*}
y y^{\prime }&=3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.411 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| \begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.260 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.263 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.287 |
|
| \begin{align*}
y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.774 |
|
| \begin{align*}
x y y^{\prime }+x^{6}-2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.008 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.479 |
|
| \begin{align*}
y^{3}+2 x y^{3}+1+3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
y^{\prime }-4 y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.484 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.467 |
|
| \begin{align*}
y^{5} y^{\prime }+5 y^{6}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.159 |
|
| \begin{align*}
y^{\prime }+y x&=y^{5} x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.847 |
|
| \begin{align*}
y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| \begin{align*}
x y y^{\prime }+2 x +\frac {y^{2}}{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.486 |
|
| \begin{align*}
-y^{2}+x^{2} y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.414 |
|
| \begin{align*}
3 y^{2}-2 x^{2}&=2 x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.045 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.000 |
|
| \begin{align*}
y^{\prime }&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.175 |
|
| \begin{align*}
x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| \begin{align*}
x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\
y \left (\infty \right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.170 |
|
| \begin{align*}
v v^{\prime }&=g \\
v \left (x_{0} \right ) &= v_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
1.972 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.231 |
|
| \begin{align*}
x^{2}+2 y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.590 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.015 |
|
| \begin{align*}
v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\
v \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.652 |
|
| \begin{align*}
1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.145 |
|
| \begin{align*}
1+y^{2}+x y^{2}+\left (x^{2} y+y+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.515 |
|
| \begin{align*}
y \left (1+2 y x \right )-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| \begin{align*}
x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
s \left (2+s^{2} t \right )+2 t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.249 |
|
| \begin{align*}
y \left (2-3 y x \right )-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.868 |
|
| \begin{align*}
y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.935 |
|
| \begin{align*}
2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.582 |
|
| \begin{align*}
x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.989 |
|
| \begin{align*}
x y^{\prime }&=x^{2} y^{2}+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.404 |
|
| \begin{align*}
y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.683 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.700 |
|
| \begin{align*}
y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.968 |
|
| \begin{align*}
y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.374 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.565 |
|
| \begin{align*}
x y^{\prime }&=y-y^{3} \cos \left (x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
x y^{\prime }-y&=x^{k} y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.611 |
|
| \begin{align*}
2 x y y^{\prime }&=y^{2}-2 x^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.796 |
|
| \begin{align*}
y^{4}-2 y x +3 x^{2} y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.103 |
|
| \begin{align*}
2 y^{3}-x^{3}+3 x y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.915 |
|
| \begin{align*}
x^{2}+6 y^{2}-4 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.492 |
|
| \begin{align*}
x y^{\prime }&=x^{3} y^{3}-2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.941 |
|
| \begin{align*}
4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.272 |
|
| \begin{align*}
y^{\prime }&=2 y \left (-1+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.717 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.798 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.770 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| \begin{align*}
y^{\prime }&=y \left (t +y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.025 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| \begin{align*}
y^{\prime }&=y \left (t +y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.592 |
|
| \begin{align*}
y^{\prime }&=2 y \left (5-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
\frac {y^{\prime }}{y}&=y-t \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| \begin{align*}
{\mathrm e}^{t} y^{\prime }&=y^{3}-y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.739 |
|
| \begin{align*}
y y^{\prime }&=t \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.621 |
|
| \begin{align*}
1-y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.438 |
|
| \begin{align*}
y^{3} y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.586 |
|
| \begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.258 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.888 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
45.994 |
|
| \begin{align*}
y^{\prime }&=4 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.915 |
|
| \begin{align*}
y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| \begin{align*}
t y y^{\prime }+t^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.097 |
|
| \begin{align*}
2 y y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.184 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.830 |
|
| \begin{align*}
y^{\prime }&=4 t y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
23.362 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
65.507 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{y t} \\
y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.294 |
|
| \begin{align*}
-y+y^{\prime }&=t y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.404 |
|
| \begin{align*}
y+y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
7.162 |
|
| \begin{align*}
y t +y^{\prime }&=t y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.927 |
|
| \begin{align*}
y t +y^{\prime }&=t^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime }-y t&=5 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.315 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.937 |
|
| \begin{align*}
y y^{\prime }+t y^{2}&=t \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.959 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.905 |
|
| \begin{align*}
y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.039 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.800 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.092 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.500 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
10.382 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.796 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.186 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.020 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (t_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.525 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.635 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.957 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.776 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
y^{\prime }&=a y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.509 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.330 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.645 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.511 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.564 |
|
| \begin{align*}
y^{\prime }&=t y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.158 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.248 |
|
| \begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.861 |
|
| \begin{align*}
p^{\prime }&=p \left (1-p\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.595 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.327 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.035 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.695 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.764 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.377 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.834 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.825 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.934 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.864 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.938 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.672 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
25.421 |
|
| \begin{align*}
y^{\prime }&=y \left (-3+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.683 |
|
| \begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.336 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.670 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
61.079 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.046 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.767 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.624 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.817 |
|
| \begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.081 |
|
| \begin{align*}
y^{\prime }&=-\frac {1}{2 y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
60.362 |
|
| \begin{align*}
2 x y y^{\prime }-1-y^{2}&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.188 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.868 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.964 |
|
| \begin{align*}
x^{3}+x y^{4}+2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| \begin{align*}
x^{\prime }-\frac {2 x}{y}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.639 |
|
| \begin{align*}
y y^{\prime }+y^{2} \cot \left (x \right )&=\csc \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.763 |
|
| \begin{align*}
x y^{\prime }+y&=3 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.421 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }+y&=5 \left (x -2\right )^{2} \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.454 |
|
| \begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.609 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.310 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.695 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.928 |
|
| \begin{align*}
-x y^{\prime }+y&=a y^{2}+a y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.030 |
|
| \begin{align*}
3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=x^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.567 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.856 |
|
| \begin{align*}
2 x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.747 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| \begin{align*}
x y y^{\prime }&=2 y^{2}-3 x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.950 |
|
| \begin{align*}
x y^{2}+x^{2} y y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| \begin{align*}
y^{\prime }+y&=\epsilon y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
y y^{\prime }&=-2 x^{3}+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.014 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| \begin{align*}
y^{\prime }&=3 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.979 |
|
| \begin{align*}
x y^{2} y^{\prime }+y^{3}&=\frac {1}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| \begin{align*}
y&=x y^{\prime }+y^{2} \sin \left (x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.750 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.317 |
|
| \begin{align*}
y^{\prime }&=y+3 y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
y^{\prime }&=\frac {x -1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +1}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.523 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
\ln \left (x \right )+y^{3}-3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.169 |
|
| \begin{align*}
y^{\prime }&=y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
6.056 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.157 |
|
| \begin{align*}
8 x y^{\prime }-y&=-\frac {1}{y^{3} \sqrt {x +1}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.224 |
|
| \begin{align*}
x^{2} y^{\prime }+2 x^{3} y&=y^{2} \left (x^{3}+1\right ) \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.162 |
|
| \begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \left (x \cos \left (x \right )-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.665 |
|
| \begin{align*}
y^{\prime }+\frac {y \left (x +\frac {1}{2}\right )}{x^{2}+x +1}&=\frac {\left (-x^{2}+1\right ) y^{2}}{\left (x^{2}+x +1\right )^{{3}/{2}}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.355 |
|
| \begin{align*}
3 y^{\prime }+\frac {y \left (a^{2}+x^{2}\right )}{x \left (-a^{2}+x^{2}\right )}&=\frac {x \left (-a^{2}+3 x^{2}\right )}{y^{2} \left (-a^{2}+x^{2}\right )} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.866 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x^{2} y^{2}+y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.906 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x +1}&=-\frac {\left (x +1\right )^{3} y^{3}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| \begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.372 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.550 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.155 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.818 |
|
| \begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.799 |
|
| \begin{align*}
y+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.335 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.127 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
3 y^{\prime }&=\frac {4 x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.126 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.945 |
|
| \begin{align*}
4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.802 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=-\frac {1}{y^{{3}/{2}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.450 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {1}{x^{4} y^{{3}/{4}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.013 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2}}{x}+\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.374 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
269.159 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.293 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
x^{2}+y^{2} y^{\prime }&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.161 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.710 |
|
| \begin{align*}
x x^{\prime }+t&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
y^{2}-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.074 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.127 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{3}+y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.151 |
|
| \begin{align*}
2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
\left (x +1\right ) \left (y^{\prime }+y^{2}\right )&=-y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \begin{align*}
y^{\prime }&=y^{4} \cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{2}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| \begin{align*}
x y y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
x y^{\prime }-2 x^{2} \sqrt {y}&=4 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
x y^{\prime }+2 y+x^{5} y^{3} {\mathrm e}^{x}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
2 y^{\prime }-\frac {x}{y}&=\frac {x y}{x^{2}-1} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| \begin{align*}
\left (x +1\right ) \left (y y^{\prime }-1\right )&=y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| \begin{align*}
x^{2}+y^{2}+x +y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.930 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| \begin{align*}
y-\frac {1}{x}+\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.627 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.323 |
|
| \begin{align*}
y-y^{\prime }&=x y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.337 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.706 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.649 |
|
| \begin{align*}
y^{\prime }+y x -x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.389 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 x y^{2}&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.262 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.539 |
|
| \begin{align*}
x y^{2}-x +\left (y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.655 |
|
| \begin{align*}
y y^{\prime }+y^{2} \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.221 |
|
| \begin{align*}
y^{\prime }+x y^{{1}/{3}}&=3 y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.929 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.359 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.534 |
|
| \begin{align*}
x y^{\prime }&=2 \sqrt {y}\, \cos \left (x \right )-2 y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.623 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}+2 x y \ln \left (x \right )+1&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.520 |
|
| \begin{align*}
y^{2} y^{\prime }+x^{2} \sin \left (x \right )^{3}&=y^{3} \cot \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.934 |
|
| \begin{align*}
\left (y^{\prime }-x \sqrt {y}\right ) \left (x^{2}-1\right )&=y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.374 |
|
| \begin{align*}
y^{2}&=\left (x y y^{\prime }+1\right ) \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.666 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+y^{3}&=y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-x}{2 \left (x +1\right ) y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
✓ |
2.955 |
|
| \begin{align*}
y^{\prime }-8 x \sqrt {y}&=\frac {4 x y}{x^{2}-1} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.628 |
|