| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.034 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.044 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right )-2 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=3 x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=2 \sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.518 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=3+x \,{\mathrm e}^{x}+x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2+x +{\mathrm e}^{x} x^{2}+x \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }&=1+x \,{\mathrm e}^{x}+2 x \cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=x +x \,{\mathrm e}^{x}+x \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime \prime }-y&=1+x \,{\mathrm e}^{x}+{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.285 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x+y+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \begin{align*}
x^{\prime }+x&=1 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x^{\prime }-x&=1 \\
x \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
x^{\prime }&=2 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-5 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=-2 x+y+x \,y^{2} \\
y^{\prime }&=-7 x-2 y-7 y \,x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \begin{align*}
x^{\prime }&=-y+x^{2} y^{3} \\
y^{\prime }&=x-x^{3} y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }&=y+x^{3} \\
y^{\prime }&=x-y^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.023 |
|
| \begin{align*}
x^{\prime }&=-2 x+\sin \left (y\right ) \\
y^{\prime }&=5 \,{\mathrm e}^{x}-5-y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=2 x-y \cos \left (y\right ) \\
y^{\prime }&=3 x-2 y-x \,y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
y^{\prime \prime }+\left (1+\frac {1}{x^{2}+1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
2.360 |
|
| \begin{align*}
y^{\prime }+y&=\epsilon y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.185 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
2.710 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
x y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.361 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.607 |
|
| \begin{align*}
y y^{\prime }&=-2 x^{3}+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.014 |
|
| \begin{align*}
x y^{\prime }&=y \tan \left (\ln \left (y\right )\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.801 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x^{2}+x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
x y^{\prime }&=y+x \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.137 |
|
| \begin{align*}
x y^{\prime }-y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.868 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.937 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
y^{\prime } \ln \left (\frac {y^{\prime }}{4}\right )&=4 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.989 |
|
| \begin{align*}
x&=y^{\prime }+\arcsin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.730 |
|
| \begin{align*}
{y^{\prime }}^{2}+{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| \begin{align*}
y^{\prime }&=3 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \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+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\left (\ln \left (x \right )-\ln \left (y\right )\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.803 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.505 |
|
| \begin{align*}
x y^{\prime }+1&={\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
x y^{2} y^{\prime }+y^{3}&=\frac {1}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.584 |
|
| \begin{align*}
3 x^{2}-8 y x +2 y^{2}-\left (4 x^{2}-4 y x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.536 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.816 |
|
| \begin{align*}
y&=x y^{\prime }+y^{2} \sin \left (x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.750 |
|
| \begin{align*}
x y^{\prime }+x \ln \left (y\right ) y^{\prime }&=x \sin \left (x \right )+\ln \left (y\right ) y \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
4.714 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.471 |
|
| \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 }&=\sqrt {x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.981 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.415 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.964 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.362 |
|
| \begin{align*}
y^{\prime }&=1-\cot \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| \begin{align*}
y^{\prime }&=x +1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.671 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
y^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (2 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.191 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|