| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y x&=x^{2}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=2\\ \end {array} \]
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
10.234 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
16.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
18.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
2.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
16.960 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.921 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.164 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
16.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +\left (-n^{2}+x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.989 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -3 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
7.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=0\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&={\mathrm e}^{5 x}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.827 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=0\\ y \left (\pi \right )&=2\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\sin \left (x \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=4 t^{2}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.933 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.884 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=0\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=2\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&={\mathrm e}^{t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=0\\ y \left (1\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+5 y&=0\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&={\mathrm e}^{t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (t \right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (\pi \right )&=0\\ y^{\prime }\left (\pi \right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&=5\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+z&=t\\ z^{\prime }+4 y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }+y&=\sin \left (t \right )\\ y^{\prime }-z&={\mathrm e}^{t}\\ w+y+z^{\prime }&=1\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
1.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+z+y&=0\\ y^{\prime }+z^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime \prime }+y^{\prime }&=\cos \left (t \right )\\ y^{\prime \prime }-z&=\sin \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t}\\ -2 w^{\prime }+2 y^{\prime }+z&=0\\ 2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+z&=t\\ z^{\prime }-y&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-z&=0\\ y-z^{\prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }-w-2 y&=1\\ y^{\prime }-4 w-3 y&=-1\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }-y&=0\\ w+y^{\prime }+z&=1\\ w-y+z^{\prime }&=2 \sin \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
1.390 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-2 v&=2\\ u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }-2 z&=0\\ w^{\prime }+y^{\prime }-z&=2 t\\ w^{\prime }-2 y+z^{\prime \prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.075 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }+y+z&=-1\\ w+y^{\prime \prime }-z&=0\\ -w-y^{\prime }+z^{\prime \prime }&=0\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.075 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=8 x-2 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=8 x-2 y+{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x+3\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-9 x+6 y+t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-2 y-5 z+3\\ z^{\prime }&=y+2 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=9 x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+4\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+4\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+4\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=4 x+3 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{3}\\ x_{3}^{\prime }&=6 t\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=9 x\\ y \left (0\right )&=1\\ y^{\prime }\left (1\right )&=2\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x\\ y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (0\right )&=-1\\ y \left (\frac {\pi }{2}\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
20.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
1.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x\\ y \left (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
✗ |
9.409 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x\\ y \left (\frac {\pi }{2}\right )&=\frac {\pi }{2}\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}+5 y \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} r^{\prime }&=\sqrt {r t} \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
153.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-3 x&=\sin \left (y \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +y+\left (x -3\right ) y^{\prime }&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y x&=\sin \left (y^{\prime \prime }\right ) \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
✗ |
2.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=x\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.992 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} s^{\prime \prime }&=-9 s\\ s \left (0\right )&=9\\ s^{\prime }\left (0\right )&=18\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
75.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}&=y\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
617.556 |
|