| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| \begin{align*}
x^{\prime }&=t^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
14.314 |
|
| \begin{align*}
x^{\prime }&=t \cos \left (t^{2}\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
x^{\prime }&=\frac {t +1}{\sqrt {t}} \\
x \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \begin{align*}
x^{\prime \prime }&=-3 \sqrt {t} \\
x \left (1\right ) &= 4 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.302 |
|
| \begin{align*}
x^{\prime }&=t \,{\mathrm e}^{-2 t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{t \ln \left (t \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
\sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \begin{align*}
t x^{\prime \prime }+x^{\prime }&=1 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.046 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{-2 x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.075 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.562 |
|
| \begin{align*}
u^{\prime }&=\frac {1}{5-2 u} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.603 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \begin{align*}
Q^{\prime }&=\frac {Q}{4+Q^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.438 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.293 |
|
| \begin{align*}
y^{\prime }&=r \left (a -y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.017 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.390 |
|
| \begin{align*}
\theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.493 |
|
| \begin{align*}
\left (2 u+1\right ) u^{\prime }-t -1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.597 |
|
| \begin{align*}
R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.027 |
|
| \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*}
y^{\prime }&=\frac {1}{2 y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \begin{align*}
x^{\prime }&=\left (4 t -x\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.445 |
|
| \begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.350 |
|
| \begin{align*}
x^{\prime }&=t^{2} {\mathrm e}^{-x} \\
x \left (0\right ) &= \ln \left (2\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| \begin{align*}
x^{\prime }&=x \left (4+x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.325 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t +x} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.116 |
|
| \begin{align*}
T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\
T \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.295 |
|
| \begin{align*}
y^{\prime }&=t^{2} \tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.732 |
|
| \begin{align*}
x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.681 |
|
| \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 {t^{2}}{1-x^{2}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.259 |
|
| \begin{align*}
x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.272 |
|
| \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*}
x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \begin{align*}
\frac {t x^{\prime \prime }+x^{\prime }}{t}&=-2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| \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 }&=2 t^{3} x-6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.976 |
|
| \begin{align*}
x^{\prime }&=t -x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.874 |
|
| \begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.870 |
|
| \begin{align*}
x x^{\prime }&=1-x t \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
15.672 |
|
| \begin{align*}
{x^{\prime }}^{2}+x t&=\sqrt {t +1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
60.183 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{t}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.506 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
x^{\prime }+2 x t&={\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.240 |
|
| \begin{align*}
x^{\prime } t&=-x+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-3 x t +6 t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.000 |
|
| \begin{align*}
x^{\prime }+\frac {5 x}{t}&=t +1 \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.203 |
|
| \begin{align*}
x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.264 |
|
| \begin{align*}
R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\
R \left (1\right ) &= 3 \ln \left (2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.471 |
|
| \begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
\cos \left (\theta \right ) v^{\prime }+v&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.405 |
|
| \begin{align*}
R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\
R \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.690 |
|
| \begin{align*}
y^{\prime }+a y&=\sqrt {t +1} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| \begin{align*}
x^{\prime }&=2 x t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.854 |
|
| \begin{align*}
x^{\prime }+\frac {{\mathrm e}^{-t} x}{t}&=t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.755 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=3 t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \begin{align*}
x^{\prime }&=\left (t +x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.963 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
x^{\prime }+p \left (t \right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.874 |
|
| \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^{3}+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.758 |
|
| \begin{align*}
x^{\prime }&=-\frac {\sin \left (x\right )-\sin \left (t \right ) x}{t \cos \left (x\right )+\cos \left (t \right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
28.617 |
|
| \begin{align*}
x+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.280 |
|
| \begin{align*}
t \cot \left (x\right ) x^{\prime }&=-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.963 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| \begin{align*}
\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| \begin{align*}
\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+6 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.380 |
|
| \begin{align*}
x^{\prime \prime }-12 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.926 |
|
| \begin{align*}
2 x^{\prime \prime }+3 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \begin{align*}
\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{8}+x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 t^{3}-1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t^{2} {\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&={\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.437 |
|