| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.547 |
|
| \begin{align*}
x^{\prime }&=t^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
21.092 |
|
| \begin{align*}
x^{\prime }&=t \cos \left (t^{2}\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
x^{\prime }&=\frac {1+t}{\sqrt {t}} \\
x \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.283 |
|
| \begin{align*}
x^{\prime \prime }&=-3 \sqrt {t} \\
x \left (1\right ) &= 4 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.572 |
|
| \begin{align*}
x^{\prime }&=t \,{\mathrm e}^{-2 t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{t \ln \left (t \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
\sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.866 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
7.265 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{-2 x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.225 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.407 |
|
| \begin{align*}
u^{\prime }&=\frac {1}{5-2 u} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.056 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
Q^{\prime }&=\frac {Q}{4+Q^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.130 |
|
| \begin{align*}
y^{\prime }&=r \left (a -y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.432 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{1+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.708 |
|
| \begin{align*}
\theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.500 |
|
| \begin{align*}
\left (2 u+1\right ) u^{\prime }-1-t&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.210 |
|
| \begin{align*}
R^{\prime }&=\left (1+t \right ) \left (1+R^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.640 |
|
| \begin{align*}
y^{\prime }+y+\frac {1}{y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.006 |
|
| \begin{align*}
\left (1+t \right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.784 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.066 |
|
| \begin{align*}
x^{\prime }&=\left (4 t -x\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.226 |
|
| \begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.408 |
|
| \begin{align*}
x^{\prime }&=t^{2} {\mathrm e}^{-x} \\
x \left (0\right ) &= \ln \left (2\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.508 |
|
| \begin{align*}
x^{\prime }&=x \left (4+x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.339 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t +x} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.313 |
|
| \begin{align*}
T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\
T \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.740 |
|
| \begin{align*}
y^{\prime }&=t^{2} \tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.300 |
|
| \begin{align*}
x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.952 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
11.817 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{1-x^{2}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.166 |
|
| \begin{align*}
x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.732 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.290 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
5.507 |
|
| \begin{align*}
\frac {x^{\prime }+t x^{\prime \prime }}{t}&=-2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.703 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.347 |
|
| \begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.274 |
|
| \begin{align*}
x^{\prime }&=2 t^{3} x-6 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| \begin{align*}
\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.260 |
|
| \begin{align*}
x^{\prime }&=t -x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
13.535 |
|
| \begin{align*}
7 t^{2} x^{\prime }&=3 x-2 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.871 |
|
| \begin{align*}
x x^{\prime }&=1-t x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
15.672 |
|
| \begin{align*}
{x^{\prime }}^{2}+t x&=\sqrt {1+t} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
60.183 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{t}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.510 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| \begin{align*}
x^{\prime }+2 t x&={\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.298 |
|
| \begin{align*}
t x^{\prime }&=-x+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.764 |
|
| \begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.434 |
|
| \begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-3 t x+6 t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.426 |
|
| \begin{align*}
x^{\prime }+\frac {5 x}{t}&=1+t \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.358 |
|
| \begin{align*}
x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.969 |
|
| \begin{align*}
R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\
R \left (1\right ) &= 3 \ln \left (2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.960 |
|
| \begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.670 |
|
| \begin{align*}
\cos \left (\theta \right ) v^{\prime }+v&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.587 |
|
| \begin{align*}
R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\
R \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.249 |
|
| \begin{align*}
y^{\prime }+a y&=\sqrt {1+t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.387 |
|
| \begin{align*}
x^{\prime }&=2 t x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.250 |
|
| \begin{align*}
x^{\prime }+\frac {{\mathrm e}^{-t} x}{t}&=t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.087 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=3 t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.704 |
|
| \begin{align*}
x^{\prime }&=\left (t +x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.555 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.879 |
|
| \begin{align*}
x^{\prime }+p \left (t \right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.312 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.428 |
|
| \begin{align*}
x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.411 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.284 |
|
| \begin{align*}
t^{2} y^{\prime }+2 t y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
47.234 |
|
| \begin{align*}
x^{\prime }&=a x+b x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
32.470 |
|
| \begin{align*}
w^{\prime }&=t w+t^{3} w^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.638 |
|
| \begin{align*}
x^{3}+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \begin{align*}
t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.295 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
26.172 |
|
| \begin{align*}
x+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.695 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.262 |
|
| \begin{align*}
t \cot \left (x\right ) x^{\prime }&=-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.692 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
4.734 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.836 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.673 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
7.064 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
8.017 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 t^{3}-1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
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✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t^{2} {\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&={\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
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✓ |
3.061 |
|