| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.161 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x^{6} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| \begin{align*}
y^{\prime }-2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.764 |
|
| \begin{align*}
y^{\prime }+y&=x^{2}+2 x -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.921 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.126 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y \left (2\right ) &= -4 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 2.278 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -12 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y^{\prime }\left (1\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✗ |
✗ |
✓ |
2.036 |
|
| \begin{align*}
y^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
y^{\prime }&=x -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime }&=1+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
y^{\prime }&=4-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.389 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.800 |
|
| \begin{align*}
y^{\prime }&=-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.743 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.023 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.477 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 1.766 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.040 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.743 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
0.994 |
|
| \begin{align*}
y^{\prime }&={| y|} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.045 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.248 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.822 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.790 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.585 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{y^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.278 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y^{\prime }&=\ln \left (y-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\left (y+2\right ) \left (y-1\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.807 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.434 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{1-y} \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.211 |
|
| \begin{align*}
y^{\prime }&=\left (y x \right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
58.968 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {y-4}{x}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.326 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x}+y^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
13.977 |
|
| \begin{align*}
y^{\prime }&=4 y-5 \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \begin{align*}
y^{\prime }+3 y&=1 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.852 |
|
| \begin{align*}
y^{\prime }&=a y+b \\
y \left (c \right ) &= d \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y^{\prime }&=x^{2}+{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
y^{\prime }&=y x +\frac {1}{x^{2}+1} \\
y \left (-5\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.428 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.929 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.167 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.384 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.957 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) y+\csc \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
y^{\prime }&=-x \sqrt {1-y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.853 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (6\right ) &= -9 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.496 |
|
| \begin{align*}
y^{\prime }&=1+3 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
y^{\prime }&=x +\frac {1}{x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.371 |
|
| \begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime }&=x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.394 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime }&=3 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \begin{align*}
y^{\prime }&=1-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
y^{\prime }&=1-y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y-x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.119 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.185 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.723 |
|
| \begin{align*}
y^{\prime }&=y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.191 |
|
| \begin{align*}
y^{\prime }&=y x +x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \begin{align*}
x \,{\mathrm e}^{y}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \begin{align*}
y-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| \begin{align*}
2 y^{\prime } y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \begin{align*}
2 x y^{\prime } y+y^{2}&=-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| \begin{align*}
y^{\prime }&=\frac {-y x +1}{x^{2}} \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 1.782 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.425 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{-y x +1} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.429 |
|
| \begin{align*}
y^{\prime }&=4 y+1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
y^{\prime }&=y x +2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.424 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.940 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -1}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.688 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+{\mathrm e}^{x} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|