| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=3 x y^{\prime }+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.290 |
|
| \begin{align*}
8 x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.984 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.214 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=\left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.050 |
|
| \begin{align*}
2 x y^{\prime }+y&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.171 |
|
| \begin{align*}
x&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
x +2 y y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=y y^{\prime }+1 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
104.724 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
2 x +{y^{\prime }}^{2} x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
x&=y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.918 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
y&=y^{\prime } x \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}+1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.263 |
|
| \begin{align*}
{y^{\prime }}^{3}+x y y^{\prime }&=2 y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.636 |
|
| \begin{align*}
3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
4.083 |
|
| \begin{align*}
2 {y^{\prime }}^{5}+2 x y^{\prime }&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| \begin{align*}
\frac {1}{{y^{\prime }}^{2}}+x y^{\prime }&=2 y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
91.718 |
|
| \begin{align*}
2 y&=3 x y^{\prime }+4+2 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.124 |
|
| \begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.836 |
|
| \begin{align*}
y&=x y^{\prime }-\sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
6.382 |
|
| \begin{align*}
y&=x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.971 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {3}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| \begin{align*}
y&=x y^{\prime }-{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.486 |
|
| \begin{align*}
y&=x y^{\prime }+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| \begin{align*}
\left (-x y^{\prime }+y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.654 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-2&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.030 |
|
| \begin{align*}
y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
y^{\prime }&=y x -x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*}
Series expansion around \(x=1\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.279 |
|
| \begin{align*}
y^{\prime }&=3 x +\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*}
Series expansion around \(x=1\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*}
Series expansion around \(x=1\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (2\right ) &= 0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x +1} \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\sin \left (y\right ) \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*}
Series expansion around \(x=\frac {\pi }{2}\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.437 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }+2 y y^{\prime }&=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]] |
✓ |
✓ |
✓ |
✗ |
0.258 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.520 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.288 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
0.976 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| \begin{align*}
2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.982 |
|
| \begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| \begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.199 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
4 x^{2} \left (1-x \right ) 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]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
2 x^{2} \left (-3 x +1\right ) y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
\left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \begin{align*}
x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.174 |
|
| \begin{align*}
2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \begin{align*}
x^{2} \left (1-x \right ) 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]] |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.881 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }-y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.192 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }-y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }-2 y x&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.702 |
|
| \begin{align*}
x y^{\prime \prime }-x y^{\prime }+y&=x^{3} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.249 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=x^{2}-x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.473 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y&=x^{2}+x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.536 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.000 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.255 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y&=x -1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=6 \left (-x^{2}+1\right )^{2} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.366 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (x +2\right )^{2} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.247 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=x \left (x^{2}+x +1\right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.157 |
|