| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime \prime }-y \cos \left (x \right )&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.498 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.450 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.158 |
|
| \begin{align*}
\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \begin{align*}
2 y^{\prime \prime } x -5 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
9 y^{\prime \prime } x +14 y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
7 y^{\prime \prime } x +10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.274 |
|
| \begin{align*}
y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 3.233 |
|
| \begin{align*}
y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
0.800 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +k \left (1+k \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+k y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.871 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
\left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+t y&=0 \\
\end{align*} | [_Lienard] | ✓ | ✓ | ✓ | ✓ | 0.124 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \begin{align*}
6 y^{\prime \prime }+5 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+34 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
2 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \begin{align*}
20 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
12 y^{\prime \prime }+8 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=-t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=-3 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.246 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\frac {1}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.537 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=-4 \,{\mathrm e}^{-2 t} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.373 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }+20 y&=-2 \,{\mathrm e}^{t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y&={\mathrm e}^{t} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
y^{\prime \prime \prime }-12 y^{\prime }-16 y&={\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y&={\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y&=t^{2} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
27.691 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\tan \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.450 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \ln \left (t \right ) \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
y^{\prime \prime }-2 t y^{\prime }+t^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.525 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.433 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=8 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.742 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=x \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| \begin{align*}
\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
3 y^{\prime \prime } x +11 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.602 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.872 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \begin{align*}
t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime }&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.684 |
|
| \begin{align*}
4 x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \begin{align*}
9 x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= -{\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.722 |
|
| \begin{align*}
x^{\prime \prime }+64 x&=0 \\
x \left (0\right ) &= {\frac {3}{4}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.749 |
|
| \begin{align*}
x^{\prime \prime }+100 x&=0 \\
x \left (0\right ) &= -{\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.560 |
|