| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-2 y x&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.414 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
7.266 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.779 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
1.965 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.209 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \begin{align*}
-y+y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.856 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.816 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.625 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
7.425 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+\left (-n^{2}+x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.132 |
|
| \begin{align*}
x y^{\prime \prime }-3 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
5.724 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.272 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (\pi \right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 t^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.719 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.562 |
|
| \begin{align*}
y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
y^{\prime }+2 y&=2 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
y^{\prime }+5 y&=0 \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (-4+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.552 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| \begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
w^{\prime }+y&=\sin \left (t \right ) \\
y^{\prime }-z&={\mathrm e}^{t} \\
w+y+z^{\prime }&=1 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
w \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| \begin{align*}
y^{\prime \prime }+z+y&=0 \\
y^{\prime }+z^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.041 |
|
| \begin{align*}
z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\
y^{\prime \prime }-z&=\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\
-2 w^{\prime }+2 y^{\prime }+z&=0 \\
2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 2 \\
z^{\prime }\left (0\right ) &= -2 \\
w \left (0\right ) &= 1 \\
w^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
y^{\prime }+z&=t \\
z^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y^{\prime }-z&=0 \\
y-z^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
w^{\prime }-w-2 y&=1 \\
y^{\prime }-4 w-3 y&=-1 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
w \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
w^{\prime }-y&=0 \\
w+y^{\prime }+z&=1 \\
w-y+z^{\prime }&=2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
w \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| \begin{align*}
u^{\prime \prime }-2 v&=2 \\
u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1 \\
\end{align*}
With initial conditions \begin{align*}
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 2 \\
v \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
w^{\prime \prime }-2 z&=0 \\
w^{\prime }+y^{\prime }-z&=2 t \\
w^{\prime }-2 y+z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
z^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
w^{\prime \prime }+y+z&=-1 \\
w+y^{\prime \prime }-z&=0 \\
-w-y^{\prime }+z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.050 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (1\right ) &= 2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 1 \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 y-5 z+3 \\
z^{\prime }&=y+2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
✓ |
1.344 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=9 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (1\right ) &= 1 \\
x_{2} \left (1\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (1\right ) &= 0 \\
x_{2} \left (1\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=6 t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 12 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=9 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= -1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.932 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
9.872 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
31.884 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
y^{\prime }&=x^{2}+5 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.076 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
{s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.566 |
|
| \begin{align*}
r^{\prime }&=\sqrt {r t} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
28.721 |
|
| \begin{align*}
x^{\prime \prime }-3 x&=\sin \left (y \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
2 x +y+\left (x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.756 |
|
| \begin{align*}
y^{\prime \prime }+y x&=\sin \left (y^{\prime \prime }\right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
2.471 |
|
| \begin{align*}
y^{\prime }+y&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
s^{\prime \prime }&=-9 s \\
s \left (0\right ) &= 9 \\
s^{\prime }\left (0\right ) &= 18 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.626 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
218.561 |
|