| # | 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] |
✗ |
✓ |
✗ |
0.058 |
|
| \(2\) |
\begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.076 |
|
| \(3\) |
\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]] |
✗ |
✓ |
✗ |
0.132 |
|
| \(5\) |
\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]] |
✗ |
✓ |
✗ |
0.153 |
|
| \(6\) |
\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]] |
✗ |
✓ |
✗ |
0.200 |
|
| \(7\) |
\begin{align*}
x^{3} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.112 |
|
| \(8\) |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.047 |
|
| \(9\) |
\begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.066 |
|
| \(10\) |
\begin{align*}
t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.397 |
|
| \(11\) |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y&=0 \\
\end{align*}
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.695 |
|
| \(12\) |
\begin{align*}
t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.184 |
|
| \(13\) |
\begin{align*}
t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.417 |
|
| \(14\) |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y&=0 \\
\end{align*}
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.372 |
|
| \(15\) |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.164 |
|
| \(16\) |
\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 |
|
| \(17\) |
\begin{align*}
y^{\prime \prime }+\frac {y}{z^{3}}&=0 \\
\end{align*}
Series expansion around \(z=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.114 |
|
| \(18\) |
\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]] |
✗ |
✓ |
✗ |
0.185 |
|
| \(19\) |
\begin{align*}
x^{4} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.122 |
|
| \(20\) |
\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]] |
✗ |
✓ |
✗ |
0.086 |
|
| \(21\) |
\begin{align*}
y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.165 |
|
| \(22\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=x^{{3}/{2}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.102 |
|
| \(23\) |
\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]] |
✗ |
✓ |
✗ |
0.121 |
|
| \(24\) |
\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]] |
✗ |
✓ |
✗ |
0.299 |
|
| \(25\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.125 |
|
| \(26\) |
\begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (4 x +2\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]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(27\) |
\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]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(28\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.089 |
|
| \(29\) |
\begin{align*}
x y^{\prime \prime }-2 y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.513 |
|
| \(30\) |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✗ |
✓ |
✗ |
0.279 |
|
| \(31\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.257 |
|
| \(32\) |
\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]] |
✗ |
✓ |
✗ |
0.137 |
|
| \(33\) |
\begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.200 |
|
| \(34\) |
\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 (5+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.267 |
|
| \(35\) |
\begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.282 |
|
| \(36\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.161 |
|
| \(37\) |
\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]] |
✗ |
✓ |
✗ |
0.370 |
|
| \(38\) |
\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]] |
✗ |
✓ |
✗ |
0.356 |
|
| \(39\) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.121 |
|
| \(40\) |
\begin{align*}
x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.279 |
|
| \(41\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.280 |
|
| \(42\) |
\begin{align*}
x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.247 |
|
| \(43\) |
\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)]‘]] |
✗ |
✓ |
✗ |
0.266 |
|
| \(44\) |
\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]] |
✗ |
✓ |
✗ |
0.572 |
|
| \(45\) |
\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]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(46\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(47\) |
\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]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(48\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(49\) |
\begin{align*}
y^{\prime \prime }+5 x y^{\prime }+y \sqrt {x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.690 |
|
| \(50\) |
\begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.259 |
|
| \(51\) |
\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 (5+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.325 |
|
| \(52\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.211 |
|
| \(53\) |
\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]] |
✗ |
✓ |
✗ |
0.556 |
|
| \(54\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.772 |
|
| \(55\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.725 |
|
| \(56\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+x +1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.756 |
|
| \(57\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.688 |
|
| \(58\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.757 |
|
| \(59\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\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]] |
✗ |
✓ |
✗ |
0.763 |
|
| \(60\) |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.615 |
|
| \(61\) |
\begin{align*}
y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
0.234 |
|
| \(62\) |
\begin{align*}
y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
0.270 |
|
| \(63\) |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✗ |
✓ |
✗ |
0.133 |
|
| \(64\) |
\begin{align*}
y^{\prime \prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _quadrature]] |
✗ |
✓ |
✗ |
0.501 |
|
| \(65\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.687 |
|
| \(66\) |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.594 |
|
| \(67\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.654 |
|
| \(68\) |
\begin{align*}
x y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✗ |
0.193 |
|
| \(69\) |
\begin{align*}
\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.704 |
|
| \(70\) |
\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]] |
✗ |
✓ |
✗ |
0.381 |
|
| \(71\) |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.349 |
|
| \(72\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.737 |
|
| \(73\) |
\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]] |
✗ |
✓ |
✗ |
0.254 |
|
| \(74\) |
\begin{align*}
y^{\prime \prime \prime }+\sin \left (y\right ) x&=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] |
✓ |
✗ |
✗ |
0.057 |
|
| \(75\) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.066 |
|
| \(76\) |
\begin{align*}
x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.158 |
|
| \(77\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.283 |
|
| \(78\) |
\begin{align*}
x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.135 |
|
| \(79\) |
\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)]‘]] |
✗ |
✓ |
✗ |
0.142 |
|
| \(80\) |
\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]] |
✗ |
✓ |
✗ |
0.179 |
|
| \(81\) |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
[_Bessel] |
✗ |
✓ |
✓ |
0.161 |
|
| \(82\) |
\begin{align*}
x^{4} y^{\prime \prime }+x y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.079 |
|
| \(83\) |
\begin{align*}
x y^{\prime \prime }-x y^{\prime }+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]] |
✓ |
✓ |
✗ |
3.735 |
|
| \(84\) |
\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]] |
✗ |
✓ |
✗ |
0.321 |
|
| \(85\) |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
0.206 |
|
| \(86\) |
\begin{align*}
t x^{\prime \prime }&=x t +1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.864 |
|
| \(87\) |
\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]] |
✗ |
✓ |
✗ |
0.472 |
|
| \(88\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.429 |
|
| \(89\) |
\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]] |
✗ |
✓ |
✗ |
1.076 |
|
| \(90\) |
\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]] |
✗ |
✓ |
✗ |
0.467 |
|
| \(91\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=4 \ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.062 |
|
| \(92\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }-y&=-\ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.053 |
|
| \(93\) |
\begin{align*}
2 y^{\prime \prime \prime }+x y^{\prime \prime }+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]] |
✓ |
✓ |
✗ |
0.054 |
|
| \(94\) |
\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]] |
✗ |
✓ |
✗ |
0.351 |
|
| \(95\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.226 |
|
| \(96\) |
\begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.349 |
|
| \(97\) |
\begin{align*}
y^{\prime \prime \prime }-y \sin \left (x \right )&=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]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(98\) |
\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]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(99\) |
\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]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(100\) |
\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]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(101\) |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✗ |
0.018 |
|
| \(102\) |
\begin{align*}
y^{\prime \prime \prime }-2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.024 |
|
| \(103\) |
\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]] |
✗ |
✓ |
✗ |
0.158 |
|
| \(104\) |
\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]] |
✗ |
✓ |
✗ |
0.219 |
|
| \(105\) |
\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]] |
✗ |
✓ |
✗ |
0.104 |
|
| \(106\) |
\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]] |
✓ |
✓ |
✗ |
0.026 |
|
| \(107\) |
\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]] |
✓ |
✓ |
✗ |
0.029 |
|
| \(108\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.026 |
|
| \(109\) |
\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]] |
✗ |
✓ |
✗ |
0.029 |
|
| \(110\) |
\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]] |
✗ |
✓ |
✗ |
0.028 |
|
| \(111\) |
\begin{align*}
x^{2} y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.062 |
|
| \(112\) |
\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]] |
✗ |
✓ |
✗ |
0.243 |
|
| \(113\) |
\begin{align*}
y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.060 |
|