| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.004 |
|
| \begin{align*}
y^{\prime }&=-2 y+8 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.691 |
|
| \begin{align*}
y^{\prime }&=5 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.341 |
|
| \begin{align*}
y^{\prime }-9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.492 |
|
| \begin{align*}
y^{\prime }+9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.510 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.629 |
|
| \begin{align*}
y^{\prime }-4 y&=-8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.497 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.524 |
|
| \begin{align*}
y^{\prime }+2 y&=6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.817 |
|
| \begin{align*}
y^{\prime }+2 y&=-6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.041 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.906 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.583 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -T \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.727 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.309 |
|
| \begin{align*}
y+y^{\prime }&=7 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.373 |
|
| \begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -4\right )-\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.131 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )+\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.895 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.402 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.433 |
|
| \begin{align*}
-y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.052 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.537 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.826 |
|
| \begin{align*}
y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (t -1\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.520 |
|
| \begin{align*}
-y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.934 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.291 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.383 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.588 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \,{\mathrm e}^{-4 t}+20 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.458 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.869 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
35.240 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.102 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.670 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\operatorname {Heaviside}\left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.991 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.966 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&={\mathrm e}^{c t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.728 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.339 |
|
| \begin{align*}
y^{\prime }&=2 y+3 \cos \left (t \right )+4 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.598 |
|
| \begin{align*}
y^{\prime }&=-y-\cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.728 |
|
| \begin{align*}
y^{\prime }&=y+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.581 |
|
| \begin{align*}
y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.456 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.250 |
|
| \begin{align*}
y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.741 |
|
| \begin{align*}
y^{\prime }&=2 y-{\mathrm e}^{i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.744 |
|
| \begin{align*}
z^{\prime }+4 z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.247 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.576 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.910 |
|
| \begin{align*}
y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.076 |
|
| \begin{align*}
-2 y+y^{\prime }&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.059 |
|
| \begin{align*}
-y+y^{\prime }&=\sin \left (\omega t \right )+\cos \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.195 |
|
| \begin{align*}
y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.006 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.368 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.244 |
|
| \begin{align*}
y^{\prime }&=y-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.022 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.973 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.264 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.768 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.586 |
|
| \begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.456 |
|
| \begin{align*}
y^{\prime }&=y+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.202 |
|
| \begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.220 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.832 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.827 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
19.108 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.807 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.481 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{1+t}+10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
22.138 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{1+t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.456 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
89.326 |
|
| \begin{align*}
m y^{\prime \prime }+k y&=F \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
58.118 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.363 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.391 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
42.691 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.798 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.974 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.255 |
|
| \begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.502 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
49.868 |
|
| \begin{align*}
y^{\prime }&=y \left (1-\ln \left (y\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
21.877 |
|
| \begin{align*}
y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.574 |
|
| \begin{align*}
y^{\prime }&=\left (1-y^{2}\right ) \left (4-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
27.529 |
|
| \begin{align*}
y^{\prime }&=k \left (m^{4}-y^{4}\right ) \\
y \left (0\right ) &= \frac {m}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
53.379 |
|
| \begin{align*}
y^{\prime }&=a y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
146.645 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
37.880 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
21.544 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.019 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.463 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
49.542 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.616 |
|
| \begin{align*}
y^{\prime }&=t y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.338 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
275.803 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.412 |
|
| \begin{align*}
y^{\prime }&=y+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.470 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.510 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
276.683 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
66.892 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.111 |
|
| \begin{align*}
y^{\prime }&=t y+t +y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.686 |
|
| \begin{align*}
y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.283 |
|