| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.675 |
|
| \begin{align*}
x +2 y+2&=\left (2 x +y-1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.651 |
|
| \begin{align*}
3 x -y+1+\left (x -3 y-5\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
59.984 |
|
| \begin{align*}
6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.547 |
|
| \begin{align*}
2 x +3 y+2+\left (-x +y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.699 |
|
| \begin{align*}
x +y+4&=\left (2 x +2 y-1\right ) y^{\prime } \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.461 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.329 |
|
| \begin{align*}
3 x -y+2+\left (x +2 y+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✓ |
✓ |
58.086 |
|
| \begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
134.010 |
|
| \begin{align*}
x -2 y+3+\left (1-x +2 y\right ) y^{\prime }&=0 \\
y \left (-4\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.568 |
|
| \begin{align*}
2 x +y+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\
y \left (-\frac {1}{6}\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
16.924 |
|
| \begin{align*}
2 x +y+\left (4 x -2 y+1\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
109.997 |
|
| \begin{align*}
x +y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.081 |
|
| \begin{align*}
3 x +y+\left (x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.681 |
|
| \begin{align*}
a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
99.769 |
|
| \begin{align*}
x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.569 |
|
| \begin{align*}
3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.997 |
|
| \begin{align*}
2 y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
96.760 |
|
| \begin{align*}
\cos \left (x \right ) y-2 \sin \left (y\right )&=\left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime } \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
19.356 |
|
| \begin{align*}
\frac {2 y x -1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.813 |
|
| \begin{align*}
y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| \begin{align*}
3 y \sin \left (x \right )-\cos \left (y\right )+\left (\sin \left (y\right ) x -3 \cos \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
30.344 |
|
| \begin{align*}
x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
32.862 |
|
| \begin{align*}
\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.102 |
|
| \begin{align*}
\frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
31.155 |
|
| \begin{align*}
\frac {y \left (2+x^{3} y\right )}{x^{3}}&=\frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.711 |
|
| \begin{align*}
y^{2} \csc \left (x \right )^{2}+6 y x -2&=\left (2 y \cot \left (x \right )-3 x^{2}\right ) y^{\prime } \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
32.872 |
|
| \begin{align*}
\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}}&=\left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
20.960 |
|
| \begin{align*}
\cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
25.441 |
|
| \begin{align*}
2 y \sin \left (y x \right )+\left (2 x \sin \left (y x \right )+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.704 |
|
| \begin{align*}
\frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
10.060 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
5.736 |
|
| \begin{align*}
\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.514 |
|
| \begin{align*}
\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
73.228 |
|
| \begin{align*}
\frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.112 |
|
| \begin{align*}
x y^{\prime }+\ln \left (x \right )-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.822 |
|
| \begin{align*}
y x +\left (x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
64.186 |
|
| \begin{align*}
\left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.432 |
|
| \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*}
\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.063 |
|
| \begin{align*}
y \left (y-x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.053 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
79.918 |
|
| \begin{align*}
\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.313 |
|
| \begin{align*}
2 y x +\left (y-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.592 |
|
| \begin{align*}
y&=x \left (x^{2} y-1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.589 |
|
| \begin{align*}
{\mathrm e}^{x} y^{\prime }&=2 x y^{2}+y \,{\mathrm e}^{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.833 |
|
| \begin{align*}
\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
66.040 |
|
| \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*}
\left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.387 |
|
| \begin{align*}
x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
31.999 |
|
| \begin{align*}
\left (x^{2}+y^{2}-2 y\right ) y^{\prime }&=2 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✗ |
✓ |
✓ |
3.863 |
|
| \begin{align*}
y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✗ |
✗ |
✗ |
38.757 |
|
| \begin{align*}
y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✗ |
✗ |
24.454 |
|
| \begin{align*}
x y^{\prime }+2 y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.799 |
|
| \begin{align*}
y^{\prime }-y x&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.258 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.711 |
|
| \begin{align*}
y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.581 |
|
| \begin{align*}
x^{\prime }+x&={\mathrm e}^{-y} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.179 |
|
| \begin{align*}
y x^{\prime }+\left (y +1\right ) x&={\mathrm e}^{y} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.053 |
|
| \begin{align*}
x y^{\prime }-2 x^{4}-2 y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.355 |
|
| \begin{align*}
1&=\left (x +{\mathrm e}^{y}\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.389 |
|
| \begin{align*}
y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
x y^{\prime }&=5 y+x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.484 |
|
| \begin{align*}
x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| \begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
7.624 |
|
| \begin{align*}
2 y&=\left (y^{4}+x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.592 |
|
| \begin{align*}
\cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \begin{align*}
\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right )&=\cos \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.671 |
|
| \begin{align*}
y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.794 |
|
| \begin{align*}
y^{2}+1+\left (2 y x -y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.106 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )-\sec \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.644 |
|
| \begin{align*}
y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.361 |
|
| \begin{align*}
2 y-y x -3+x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
y+2 \left (x -2 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
24.763 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y&=0 \\
y \left (0\right ) &= -6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| \begin{align*}
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*}
\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
3.765 |
|
| \begin{align*}
\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| \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*}
\csc \left (y\right ) \cot \left (y\right ) y^{\prime }&=\csc \left (y\right )+{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.731 |
|
| \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*}
\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.940 |
|
| \begin{align*}
\left (x \tan \left (y\right )^{2}+x \right ) y^{\prime }&=2 x^{2}+\tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
3.738 |
|
| \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*}
y^{\prime }&=x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.346 |
|
| \begin{align*}
2 y&=\left (x^{2} y^{4}+x \right ) y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.859 |
|