| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.146 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
x y^{\prime \prime }-2 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.598 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.460 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
y^{\prime }&=a f \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime }&=x +\sin \left (x \right )+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.969 |
|
| \begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.929 |
|
| \begin{align*}
y^{\prime }&=a +b x +c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| \begin{align*}
y^{\prime }&=a \cos \left (b x +c \right )+k y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.861 |
|
| \begin{align*}
y^{\prime }&=a \sin \left (b x +c \right )+k y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.697 |
|
| \begin{align*}
y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.723 |
|
| \begin{align*}
y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.580 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.345 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )+\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.112 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )-\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.085 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-\cos \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.966 |
|
| \begin{align*}
y^{\prime }&=y \cot \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.397 |
|
| \begin{align*}
y^{\prime }&=1-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
y^{\prime }&=x \csc \left (x \right )-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.970 |
|
| \begin{align*}
y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.616 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )-y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.042 |
|
| \begin{align*}
y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.948 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.335 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.905 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| \begin{align*}
y^{\prime }&=y \tan \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )-y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )-y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.278 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )+2 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.211 |
|
| \begin{align*}
y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.877 |
|
| \begin{align*}
y^{\prime }&=\csc \left (x \right )+3 y \tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.093 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.850 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.440 |
|
| \begin{align*}
y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
✗ |
3.056 |
|
| \begin{align*}
y^{\prime }+1-x&=y \left (x +y\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.121 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.226 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.749 |
|
| \begin{align*}
y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.599 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
y^{\prime }&=1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.560 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-\left (\sin \left (x \right )-y\right ) y \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.982 |
|
| \begin{align*}
y^{\prime }&=\cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.320 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.352 |
|
| \begin{align*}
y^{\prime }&=\left (3+x -4 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
14.872 |
|
| \begin{align*}
y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
23.953 |
|
| \begin{align*}
y^{\prime }&=3 a +3 b x +3 b y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| \begin{align*}
y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.769 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
30.832 |
|
| \begin{align*}
y^{\prime }&=a +b x +c y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.378 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.619 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
36.770 |
|
| \begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.692 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+a y+b y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
5.418 |
|
| \begin{align*}
y^{\prime }&=1+a \left (x -y\right ) y \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.340 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
6.923 |
|
| \begin{align*}
y^{\prime }&=x y \left (y+3\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.349 |
|
| \begin{align*}
y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
5.754 |
|
| \begin{align*}
y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
4.739 |
|
| \begin{align*}
y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
5.757 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.109 |
|
| \begin{align*}
y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.178 |
|
| \begin{align*}
y^{\prime }&=a \,x^{m}+b \,x^{n} y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
21.935 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.178 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y^{2}\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| \begin{align*}
y^{\prime }+4 \csc \left (x \right )&=\left (3-\cot \left (x \right )\right ) y+\sin \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.041 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right )+\left (-1+\sin \left (x \right )\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.457 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.872 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
12.605 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.682 |
|
| \begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
10.120 |
|
| \begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
7.318 |
|
| \begin{align*}
y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
10.317 |
|
| \begin{align*}
y^{\prime }&=y \left (a +b y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.643 |
|
| \begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
35.437 |
|
| \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 }&=\left (a +b x y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
11.964 |
|
| \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 |
|