| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.053 |
|
| \(2\) |
\begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.078 |
|
| \(3\) |
\begin{align*}
x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.271 |
|
| \(4\) |
\begin{align*}
3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.139 |
|
| \(5\) |
\begin{align*}
x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.147 |
|
| \(6\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.203 |
|
| \(7\) |
\begin{align*}
x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.115 |
|
| \(8\) |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.064 |
|
| \(9\) |
\begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.102 |
|
| \(10\) |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*}
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.219 |
|
| \(11\) |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\
\end{align*}
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.509 |
|
| \(12\) |
\begin{align*}
t^{3} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.118 |
|
| \(13\) |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*}
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.282 |
|
| \(14\) |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\
\end{align*}
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.547 |
|
| \(15\) |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.122 |
|
| \(16\) |
\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]] |
✗ |
✓ |
✗ |
0.244 |
|
| \(17\) |
\begin{align*}
y^{\prime \prime }+\frac {y}{z^{3}}&=0 \\
\end{align*}
Series expansion around \(z=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.163 |
|
| \(18\) |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.144 |
|
| \(19\) |
\begin{align*}
x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.349 |
|
| \(20\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.418 |
|
| \(21\) |
\begin{align*}
y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
1.500 |
|
| \(22\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=x^{{3}/{2}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.497 |
|
| \(23\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=\sqrt {x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.589 |
|
| \(24\) |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.081 |
|
| \(25\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.408 |
|
| \(26\) |
\begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.089 |
|
| \(27\) |
\begin{align*}
x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.082 |
|
| \(28\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.279 |
|
| \(29\) |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
10.527 |
|
| \(30\) |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✗ |
✓ |
✗ |
1.080 |
|
| \(31\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.178 |
|
| \(32\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.458 |
|
| \(33\) |
\begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.584 |
|
| \(34\) |
\begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.709 |
|
| \(35\) |
\begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.894 |
|
| \(36\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.490 |
|
| \(37\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
1.227 |
|
| \(38\) |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.859 |
|
| \(39\) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.303 |
|
| \(40\) |
\begin{align*}
x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.671 |
|
| \(41\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.514 |
|
| \(42\) |
\begin{align*}
x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.586 |
|
| \(43\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.667 |
|
| \(44\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
1.484 |
|
| \(45\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.101 |
|
| \(46\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.091 |
|
| \(47\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.102 |
|
| \(48\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.092 |
|
| \(49\) |
\begin{align*}
y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.895 |
|
| \(50\) |
\begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.645 |
|
| \(51\) |
\begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.738 |
|
| \(52\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.526 |
|
| \(53\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
1.500 |
|
| \(54\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.586 |
|
| \(55\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.540 |
|
| \(56\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+x +1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.619 |
|
| \(57\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.549 |
|
| \(58\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.617 |
|
| \(59\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.609 |
|
| \(60\) |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.391 |
|
| \(61\) |
\begin{align*}
y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
1.070 |
|
| \(62\) |
\begin{align*}
y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
1.105 |
|
| \(63\) |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✗ |
✓ |
✗ |
0.764 |
|
| \(64\) |
\begin{align*}
y^{\prime \prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _quadrature]] |
✗ |
✓ |
✗ |
1.641 |
|
| \(65\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
2.217 |
|
| \(66\) |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.013 |
|
| \(67\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.265 |
|
| \(68\) |
\begin{align*}
y^{\prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✗ |
1.187 |
|
| \(69\) |
\begin{align*}
\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.987 |
|
| \(70\) |
\begin{align*}
\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.531 |
|
| \(71\) |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.490 |
|
| \(72\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
1.054 |
|
| \(73\) |
\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]] |
✗ |
✓ |
✗ |
0.167 |
|
| \(74\) |
\begin{align*}
y^{\prime \prime \prime }+x \sin \left (y\right )&=0 \\
y \left (0\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[NONE] |
✓ |
✗ |
✗ |
0.059 |
|
| \(75\) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.148 |
|
| \(76\) |
\begin{align*}
x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.348 |
|
| \(77\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.690 |
|
| \(78\) |
\begin{align*}
x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.316 |
|
| \(79\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.337 |
|
| \(80\) |
\begin{align*}
y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.459 |
|
| \(81\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
[_Bessel] |
✗ |
✓ |
✓ |
0.359 |
|
| \(82\) |
\begin{align*}
x^{4} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.260 |
|
| \(83\) |
\begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.442 |
|
| \(84\) |
\begin{align*}
x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.918 |
|
| \(85\) |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
0.512 |
|
| \(86\) |
\begin{align*}
t x^{\prime \prime }&=t x+1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
1.793 |
|
| \(87\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.691 |
|
| \(88\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.127 |
|
| \(89\) |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
1.977 |
|
| \(90\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.175 |
|
| \(91\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.102 |
|
| \(92\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x -y&=-\ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.119 |
|
| \(93\) |
\begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.127 |
|
| \(94\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.736 |
|
| \(95\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.570 |
|
| \(96\) |
\begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.819 |
|
| \(97\) |
\begin{align*}
y^{\prime \prime \prime }-\sin \left (x \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.148 |
|
| \(98\) |
\begin{align*}
y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.164 |
|
| \(99\) |
\begin{align*}
y^{\prime \prime \prime }-3 x^{2} y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.144 |
|
| \(100\) |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+2 y^{\prime }-x^{3} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.151 |
|
| \(101\) |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✗ |
0.125 |
|
| \(102\) |
\begin{align*}
y^{\prime \prime \prime }-2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.126 |
|
| \(103\) |
\begin{align*}
x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.037 |
|
| \(104\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.977 |
|
| \(105\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.817 |
|
| \(106\) |
\begin{align*}
y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.158 |
|
| \(107\) |
\begin{align*}
\left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.158 |
|
| \(108\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.147 |
|
| \(109\) |
\begin{align*}
x^{4} y^{\prime \prime \prime }+\frac {x^{2} y^{\prime \prime }}{x +1}-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.161 |
|
| \(110\) |
\begin{align*}
x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{x +1}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.162 |
|
| \(111\) |
\begin{align*}
x^{2} y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.589 |
|
| \(112\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.599 |
|
| \(113\) |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime } x +\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.234 |
|