| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.350 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.612 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.897 |
|
| \begin{align*}
x y^{\prime }&=x^{2} y^{2}-y+1 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.556 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \left (2+x y^{\prime }-4 y^{2} y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
✗ |
2.747 |
|
| \begin{align*}
Q^{\prime \prime }+k Q&=e \left (t \right ) \\
Q \left (0\right ) &= q_{0} \\
Q^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| \begin{align*}
y^{\prime \prime }&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| \begin{align*}
y^{\prime \prime }+y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.062 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=12 t \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 20 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
t y^{\prime \prime }-t y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.713 |
|
| \begin{align*}
y^{\prime }+2 y&=5 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.463 |
|
| \begin{align*}
y^{\prime \prime }+y&=3 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.081 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.041 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
y^{\prime }&=y x \\
y \left (0\right ) &= 5 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
2 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.258 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x={\frac {1}{2}}\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| \begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
y^{\prime }+y&=x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| \begin{align*}
2 y^{\prime }+y x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.817 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \begin{align*}
y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \begin{align*}
y^{\prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.987 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| \begin{align*}
y^{\prime \prime }+y \,{\mathrm e}^{x}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.645 |
|
| \begin{align*}
2 x y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.612 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.120 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
8.762 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
-6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
11.793 |
|
| \begin{align*}
U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\
\end{align*}
Series expansion around \(r=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.828 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=5 \sqrt {x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.213 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=2 x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.937 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=4 x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.379 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
11.935 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-8\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
1.672 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (3 x^{2}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.787 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (2 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.882 |
|
| \begin{align*}
v^{\prime \prime }+v&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }-i x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.451 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
8.344 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\
y \left (\frac {1}{2}\right ) &= 10 \\
\end{align*}
Series expansion around \(x={\frac {1}{2}}\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (-3 x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.650 |
|
| \begin{align*}
y^{\prime }&=x \\
x^{\prime }&=-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| \begin{align*}
u^{\prime }&=2 v-1 \\
v^{\prime }&=1+2 u \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
y^{\prime \prime }&=x \\
y^{\prime \prime }&=y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.098 |
|
| \begin{align*}
y^{\prime \prime }&=x-2 \\
y^{\prime \prime }&=y+2 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
y^{\prime }+6 y&=x^{\prime } \\
3 x-x^{\prime }&=2 y^{\prime } \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
x^{\prime }+x+2 y&=1 \\
2 x+y^{\prime }-2 y&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.268 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right ) \\
x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.471 |
|
| \begin{align*}
x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\
y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= -24 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
x^{\prime }-2 y^{\prime }&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }&=\sqrt {t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x^{\prime }+3 y^{\prime }&=x y \\
3 x^{\prime }-y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.087 |
|
| \begin{align*}
r^{\prime \prime }\left (t \right )&=r \left (t \right )+y \\
y^{\prime \prime }&=5 r \left (t \right )-3 y+t^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
x y^{\prime }+y x^{\prime }&=t^{2} \\
2 x^{\prime \prime }-y^{\prime }&=5 t \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.108 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\
y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
y \left (0\right ) &= -{\frac {9}{2}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
z^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| \begin{align*}
x^{\prime }&=y z \\
y^{\prime }&=x z \\
z^{\prime }&=x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.095 |
|
| \begin{align*}
x^{\prime }&=x y \\
y^{\prime }&=1+y^{2} \\
z^{\prime }&=z \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.096 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+z^{\prime } t +z&=t \\
t y^{\prime }+z&=\ln \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.078 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
6.848 |
|