| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=y+3 y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.069 |
|
| \begin{align*}
8 x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
57.812 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.053 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=\left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.488 |
|
| \begin{align*}
x^{2}-3 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.844 |
|
| \begin{align*}
2 y^{\prime } x +y&=x {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.969 |
|
| \begin{align*}
x&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| \begin{align*}
x +2 y y^{\prime }&=x {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| \begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.604 |
|
| \begin{align*}
{y^{\prime }}^{3} x&=y y^{\prime }+1 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
125.045 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
2 x +x {y^{\prime }}^{2}&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| \begin{align*}
x&=y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.921 |
|
| \begin{align*}
4 x {y^{\prime }}^{2}+2 y^{\prime } x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.145 |
|
| \begin{align*}
y&=y^{\prime } x \left (1+y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.455 |
|
| \begin{align*}
2 {y^{\prime }}^{3} x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.433 |
|
| \begin{align*}
{y^{\prime }}^{3}+y y^{\prime } x&=2 y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.970 |
|
| \begin{align*}
3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
6.466 |
|
| \begin{align*}
2 {y^{\prime }}^{5}+2 y^{\prime } x&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.833 |
|
| \begin{align*}
\frac {1}{{y^{\prime }}^{2}}+y^{\prime } x&=2 y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
142.069 |
|
| \begin{align*}
2 y&=3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
52.917 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.140 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
8.274 |
|
| \begin{align*}
y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
6.669 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.703 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.181 |
|
| \begin{align*}
y&=y^{\prime } x +{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
5.208 |
|
| \begin{align*}
\left (-y^{\prime } x +y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.914 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-2&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.690 |
|
| \begin{align*}
y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y} \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
y^{\prime }&=y x -x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
y^{\prime }&=y^{2} x^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime }&=3 x +\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} Series expansion around \(x=1\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (2\right ) &= 0 \\
\end{align*} Series expansion around \(x=2\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x +1} \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.506 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.558 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.643 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.372 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.326 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.231 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.131 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.384 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.140 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.189 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \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]] |
✗ |
✗ |
✓ |
✗ |
0.276 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (3+2 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \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]] |
✓ |
✓ |
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✓ |
1.220 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.156 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
4.566 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
4.526 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
4.482 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }-y&=x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.653 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }-y&=x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.622 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-2 y x&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
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✗ |
0.908 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
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✗ |
3.666 |
|
| \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]] |
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✓ |
✗ |
0.629 |
|
| \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]] |
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✓ |
✗ |
2.969 |
|
| \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]] |
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✓ |
✗ |
1.175 |
|
| \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]] |
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✗ |
1.430 |
|
| \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]] |
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✗ |
1.233 |
|
| \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]] |
✓ |
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✗ |
1.127 |
|
| \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]] |
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✗ |
1.249 |
|
| \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]] |
✓ |
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✗ |
0.496 |
|
| \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]] |
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✗ |
1.545 |
|
| \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]] |
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✓ |
✗ |
1.357 |
|