| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
y \left (3\right ) &= 2 \\
y^{\prime }\left (3\right ) &= 0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y x&=0 \\
y \left (3\right ) &= 1 \\
y^{\prime }\left (3\right ) &= -2 \\
\end{align*} Series expansion around \(x=3\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
3.712 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+\frac {y}{16}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
0.721 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{16}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{3}+x^{2}+x \right ) y^{\prime }+\left (4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {2}{3}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.610 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.595 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-3\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{4}-4 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| \begin{align*}
\left (x -1\right ) \left (2+x \right ) y^{\prime \prime }+\left (x +\frac {1}{2}\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
\left (x^{2}-\frac {1}{4}\right ) y^{\prime \prime }+2 y^{\prime }-6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.341 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= B \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
4.756 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.054 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
3.983 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.709 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\ln \left (x \right ) \\
y \left (1\right ) &= A \\
y \left (2\right ) &= B \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.058 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
y \left (0\right ) &= \operatorname {c1} \\
y \left (L \right ) &= \operatorname {c2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
-\frac {u^{\prime \prime }}{2}&=x \\
u \left (0\right ) &= 0 \\
u \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✗ |
1.957 |
|
| \begin{align*}
-\frac {u^{\prime \prime }}{2}&=x \\
u \left (0\right ) &= 0 \\
u \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✗ |
1.203 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime }&=y^{2}-x^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.035 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-\sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=\sin \left (x_{1}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{1}^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=-3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
x^{\prime }&=4 x-6 y \\
y^{\prime }&=8 x-10 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+x y \\
y^{\prime }&=6 x-7 y-x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2} \\
y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| \begin{align*}
x^{\prime }&=y+x^{2}-x y \\
y^{\prime }&=-2 x+3 y+y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.027 |
|
| \begin{align*}
x^{\prime }&=-x-x^{2}+y^{2} \\
y^{\prime }&=-y+2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.050 |
|