| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 x^{2} y+{y^{\prime }}^{2}&=x^{3} y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=y+3 y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.927 |
|
| \begin{align*}
8 x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.165 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.206 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=\left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
x^{2}-3 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
1.116 |
|
| \begin{align*}
2 y^{\prime } x +y&=x {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.160 |
|
| \begin{align*}
x&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.301 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
x +2 y^{\prime } y&=x {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \begin{align*}
4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=y^{\prime } y+1 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.390 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
2 x +x {y^{\prime }}^{2}&=2 y^{\prime } y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.982 |
|
| \begin{align*}
x&=y^{\prime } y+{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.284 |
|
| \begin{align*}
4 x {y^{\prime }}^{2}+2 y^{\prime } x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
y&=y^{\prime } x \left (1+y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}+1&=y {y^{\prime }}^{2} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _dAlembert] | ✓ | ✓ | ✓ | ✗ | 1.905 |
|
| \begin{align*}
{y^{\prime }}^{3}+x y^{\prime } y&=2 y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| \begin{align*}
3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
5.277 |
|
| \begin{align*}
2 {y^{\prime }}^{5}+2 y^{\prime } x&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.507 |
|
| \begin{align*}
\frac {1}{{y^{\prime }}^{2}}+y^{\prime } x&=2 y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.825 |
|
| \begin{align*}
2 y&=3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.436 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.807 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.688 |
|
| \begin{align*}
y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.147 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.621 |
|
| \begin{align*}
y&=y^{\prime } x +{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
\left (y-y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.406 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y-2&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| \begin{align*}
y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 0.195 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y} \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
y^{\prime }&=y x -x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
y^{\prime }&=y^{2} x^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime }&=3 x +\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
y^{\prime }&=\ln \left (y x \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (2\right ) &= 0 \\
\end{align*} Series expansion around \(x=2\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.258 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x +1} \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )+\cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.420 |
|
| \begin{align*}
y^{\prime \prime }-2 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.471 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.254 |
|
| \begin{align*}
y^{\prime \prime }&=\sin \left (y\right ) \\
y \left (0\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.523 |
|
| \begin{align*}
y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.283 |
|
| \begin{align*}
y^{\prime \prime }&=\sin \left (y x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
[NONE] |
✓ |
✓ |
✓ |
✗ |
0.950 |
|
| \begin{align*}
y^{\prime \prime }&=\cos \left (y x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} Series expansion around \(x=\frac {\pi }{2}\). |
[NONE] |
✓ |
✓ |
✓ |
✗ |
0.893 |
|
| \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]] | ✓ | ✓ | ✓ | ✓ | 0.680 |
|
| \begin{align*}
3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
2 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]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.077 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
4 \left (1-x \right ) x^{2} y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.678 |
|
| \begin{align*}
x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.194 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (x^{3}+1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.118 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.185 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.057 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }-y&=x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.721 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }-y&=x \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 2.687 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-2 y x&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.713 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.665 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{2}-x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y&=x^{2}+x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.240 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y&=-2 x^{2}+x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| \begin{align*}
3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=-x^{3}+x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.151 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.970 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y&=x -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.822 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=x^{3}+1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.987 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=6 \left (-x^{2}+1\right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.416 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.214 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=x \left (x^{2}+x +1\right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.072 |
|