| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.992 |
|
| \begin{align*}
y^{\prime }&=2 y+\sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.366 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.430 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 10 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.843 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.097 |
|
| \begin{align*}
3 y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.159 |
|
| \begin{align*}
-2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| \begin{align*}
y^{\prime }+2 y&=3 t^{2}+2 t -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.302 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
y+y^{\prime }&=t^{3}+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.284 |
|
| \begin{align*}
y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.534 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.711 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.262 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{t}+t^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.357 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.036 |
|
| \begin{align*}
y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 2.687 |
|
| \begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.488 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.922 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.561 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.434 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.625 |
|
| \begin{align*}
y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.753 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.924 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.605 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.904 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.437 |
|
| \begin{align*}
y^{\prime }&=y+4 \cos \left (t^{2}\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.072 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\sqrt {t^{3}-3}}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
23.392 |
|
| \begin{align*}
y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \begin{align*}
y^{\prime }&=t^{r} y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.362 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.145 |
|
| \begin{align*}
y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 1.370 |
|
| \begin{align*}
y^{\prime }&=3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| \begin{align*}
y^{\prime }&=t^{2} \left (t^{2}+1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (y\right )^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
28.319 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (-1+t \right ) \left (3-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.450 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
10.750 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
y^{\prime }&=3-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \begin{align*}
y^{\prime }&=t y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.580 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{7 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{t^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.445 |
|
| \begin{align*}
y^{\prime }&=-5 y+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.003 |
|
| \begin{align*}
y^{\prime }&=t +\frac {2 y}{t +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.184 |
|
| \begin{align*}
y^{\prime }&=3+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.781 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.634 |
|
| \begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.091 |
|
| \begin{align*}
x^{\prime }&=-t x \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| \begin{align*}
y^{\prime }&=2 y+\cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| \begin{align*}
y^{\prime }&=3 y+2 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.598 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3}+y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.648 |
|
| \begin{align*}
y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| \begin{align*}
y^{\prime }&=2 t y+3 t \,{\mathrm e}^{t^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.062 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (t +1\right )^{2}}{\left (1+y\right )^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.899 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.309 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.784 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.920 |
|
| \begin{align*}
y^{\prime }&=y^{2}-2 y+1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
y^{\prime }&=\left (y-2\right ) \left (y+1-\cos \left (t \right )\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
6.017 |
|
| \begin{align*}
y^{\prime }&=\left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
7.754 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+1+y+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.112 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
y^{\prime }&=3-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
2.302 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
x^{\prime }&=3 y \\
y^{\prime }&=3 \pi y-\frac {x}{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
p^{\prime }&=3 p-2 q-7 r \\
q^{\prime }&=-2 p+6 r \\
r^{\prime }&=\frac {73 q}{100}+2 r \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
71.455 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 \pi y \\
y^{\prime }&=4 x-y \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.838 |
|
| \begin{align*}
x^{\prime }&=\beta y \\
y^{\prime }&=\gamma x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=2 x-5 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=3 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.502 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
x^{\prime }&=1 \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x^{\prime }&=-4 x-2 y \\
y^{\prime }&=-x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{2} \\
y^{\prime }&=x-\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=9 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.486 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.466 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.421 |
|