| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.746 |
|
| \begin{align*}
x^{\prime }&=t^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
39.881 |
|
| \begin{align*}
x^{\prime }&=t \cos \left (t^{2}\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=\frac {t +1}{\sqrt {t}} \\
x \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
x^{\prime \prime }&=-3 \sqrt {t} \\
x \left (1\right ) &= 4 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
3.294 |
|
| \begin{align*}
x^{\prime }&=t \,{\mathrm e}^{-2 t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{t \ln \left (t \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
\sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime }+t x^{\prime \prime }&=1 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.403 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.405 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{-2 x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.813 |
|
| \begin{align*}
u^{\prime }&=\frac {1}{5-2 u} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
Q^{\prime }&=\frac {Q}{4+Q^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| \begin{align*}
y^{\prime }&=r \left (a -y\right ) \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.414 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.404 |
|
| \begin{align*}
\theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.402 |
|
| \begin{align*}
\left (2 u+1\right ) u^{\prime }-t -1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.071 |
|
| \begin{align*}
R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.244 |
|
| \begin{align*}
y^{\prime }+y+\frac {1}{y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| \begin{align*}
\left (t +1\right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.314 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{\prime }&=\left (4 t -x\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.206 |
|
| \begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.395 |
|
| \begin{align*}
x^{\prime }&=t^{2} {\mathrm e}^{-x} \\
x \left (0\right ) &= \ln \left (2\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.002 |
|
| \begin{align*}
x^{\prime }&=x \left (4+x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.066 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t +x} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.367 |
|
| \begin{align*}
T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\
T \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.231 |
|
| \begin{align*}
y^{\prime }&=t^{2} \tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.517 |
|
| \begin{align*}
x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.700 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.325 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{1-x^{2}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.632 |
|
| \begin{align*}
x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.812 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 t x} \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _Bernoulli] | ✓ | ✓ | ✓ | ✓ | 13.330 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
4.887 |
|
| \begin{align*}
\frac {x^{\prime }+t x^{\prime \prime }}{t}&=-2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.873 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.387 |
|
| \begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.598 |
|
| \begin{align*}
x^{\prime }&=2 t^{3} x-6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.925 |
|
| \begin{align*}
\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| \begin{align*}
x^{\prime }&=t -x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.858 |
|
| \begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.911 |
|
| \begin{align*}
x x^{\prime }&=1-t x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
6.812 |
|
| \begin{align*}
{x^{\prime }}^{2}+t x&=\sqrt {t +1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
52.319 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{t}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \begin{align*}
x^{\prime }+2 t x&={\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.895 |
|
| \begin{align*}
t x^{\prime }&=-x+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.655 |
|
| \begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-3 t x+6 t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| \begin{align*}
x^{\prime }+\frac {5 x}{t}&=t +1 \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \begin{align*}
R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\
R \left (1\right ) &= 3 \ln \left (2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| \begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 0.999 |
|
| \begin{align*}
\cos \left (\theta \right ) v^{\prime }+v&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| \begin{align*}
R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\
R \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| \begin{align*}
y^{\prime }+a y&=\sqrt {t +1} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \begin{align*}
x^{\prime }&=2 t x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
x^{\prime }+\frac {{\mathrm e}^{-t} x}{t}&=t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=3 t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
x^{\prime }&=\left (t +x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x^{\prime }+p \left (t \right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
70.299 |
|
| \begin{align*}
x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.976 |
|
| \begin{align*}
t^{2} y^{\prime }+2 t y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \begin{align*}
x^{\prime }&=a x+b x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.280 |
|
| \begin{align*}
w^{\prime }&=t w+t^{3} w^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| \begin{align*}
x^{3}+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
1.835 |
|
| \begin{align*}
x^{\prime }&=-\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
26.258 |
|
| \begin{align*}
x+3 t x^{2} x^{\prime }&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 0.246 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.219 |
|
| \begin{align*}
t \cot \left (x\right ) x^{\prime }&=-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.407 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
6.264 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 t^{3}-1 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.380 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t^{2} {\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&={\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.973 |
|