| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.378 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (-x +2\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.702 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.271 |
|
| \begin{align*}
y^{\prime \prime }-y x&=1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } x -4 y&={\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.561 |
|
| \begin{align*}
y^{\prime \prime } x +y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.710 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.228 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+y \cos \left (x \right )&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.102 |
|
| \begin{align*}
x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| \begin{align*}
\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.825 |
|
| \begin{align*}
\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.534 |
|
| \begin{align*}
x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.500 |
|
| \begin{align*}
\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.411 |
|
| \begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.142 |
|
| \begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.691 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
3 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.874 |
|
| \begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.674 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.964 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.086 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.178 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \\
\end{align*} |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*} | [_Lienard] | ✓ | ✓ | ✓ | ✓ | 0.441 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{2}+3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 4.382 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= -6 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.087 |
|
| \begin{align*}
\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.981 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=10 x^{3}-2 x +5 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| \begin{align*}
-y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y+2 y^{\prime }&=0 \\
y \left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|