| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-30 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
y^{\prime \prime }-7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.041 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-9 y^{\prime \prime }+20 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+2 y^{\prime }+36 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-4 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&=0 \\
\end{align*} | [[_high_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.063 |
|
| \begin{align*}
y^{\left (6\right )}-5 y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }-16 y^{\prime }-32 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.041 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.040 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.039 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| \begin{align*}
-y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+16 y^{\prime }+32 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.073 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.039 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| \begin{align*}
y^{\prime }-5 y&=\sin \left (x \right ) \left (x -1\right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.105 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 1.956 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.199 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.774 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=5 x \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.429 |
|
| \begin{align*}
y^{\prime \prime }+2 y x&=x \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.486 |
|
| \begin{align*}
y^{\prime \prime \prime }&=12 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.073 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (2 x \right )+\cos \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.525 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.116 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 \left (x^{2}-3 x +2\right ) y^{\prime }+\left (x -2\right )^{2} x y&=0 \\
\end{align*} Series expansion around \(x=2\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.447 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.693 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.068 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| \begin{align*}
{\mathrm e}^{x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.721 |
|
| \begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.108 |
|
| \begin{align*}
x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.279 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= -2 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime \prime }-2 y x&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 6 \\
\end{align*} Series expansion around \(x=2\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
y^{\prime \prime }+y x&=2 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.240 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y x&=2+x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.378 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&={\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.373 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.216 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y&=x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.344 |
|
| \begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }&=x^{2}-2 x \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.316 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{-x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.304 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +x^{2} 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]] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|