| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.498 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )+y x +x^{2}-\frac {1}{4}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.625 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\tan \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \sec \left (2 x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\frac {4}{1+{\mathrm e}^{-x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=3 \,{\mathrm e}^{x} \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=14 x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=2 x^{2}+2 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.905 |
|
| \begin{align*}
y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.614 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=4 \,{\mathrm e}^{-x \left (2+x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.597 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{{5}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.691 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{4} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.138 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.439 |
|
| \begin{align*}
2 y^{\prime \prime } x +2 y^{\prime }+2 y&=\sin \left (\sqrt {x}\right ) \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 0.458 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=6 \,{\mathrm e}^{x} x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.354 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{a +1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=\cos \left (x \right ) x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.399 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.319 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=8 x^{{5}/{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.858 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.766 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=3 x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.847 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&={\mathrm e}^{x} x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.618 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=x^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y&={\mathrm e}^{x} x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.715 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=2 \left (x -1\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=x^{{5}/{2}} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| \begin{align*}
\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=\left (3 x -1\right )^{2} {\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.609 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=\left (x -1\right )^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.733 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x +1\right ) y&=\left (x -1\right )^{3} {\mathrm e}^{x} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} | [[_2nd_order, _exact, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 1.463 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=-2 x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
\left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y&=\left (2 x +3\right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.322 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
\left (3 x^{2}+1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+\left (2-3 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
\left (3 x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
y^{\prime \prime } x +\left (4+2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -3 y x&=0 \\
\end{align*} Series expansion around \(x=2\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
\left (-x +2\right ) y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= a_{0} \\
y^{\prime }\left (0\right ) &= a_{1} \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+2 \left (x -1\right )^{2} y^{\prime }+3 y&=0 \\
y \left (1\right ) &= a_{0} \\
y^{\prime }\left (1\right ) &= a_{1} \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.940 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.824 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.382 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x +\frac {y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 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]] |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\
y \left (3\right ) &= -2 \\
y^{\prime }\left (3\right ) &= 3 \\
\end{align*} Series expansion around \(x=3\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.370 |
|
| \begin{align*}
\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y&=0 \\
y \left (3\right ) &= 4 \\
y^{\prime }\left (3\right ) &= -6 \\
\end{align*} Series expansion around \(x=3\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\
y \left (4\right ) &= 3 \\
y^{\prime }\left (4\right ) &= -4 \\
\end{align*} Series expansion around \(x=4\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\
y \left (-1\right ) &= 3 \\
y^{\prime }\left (-1\right ) &= -3 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
\left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _exact, _linear, _homogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.427 |
|
| \begin{align*}
\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) 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, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 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]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\
y \left (-1\right ) &= 1 \\
y^{\prime }\left (-1\right ) &= -1 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|