| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.108 |
|
| \(2\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }&=2 y \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.156 |
|
| \(3\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.174 |
|
| \(4\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.099 |
|
| \(5\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.108 |
|
| \(6\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.172 |
|
| \(7\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.092 |
|
| \(8\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.175 |
|
| \(9\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }&=2 y \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.236 |
|
| \(10\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.351 |
|
| \(11\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \end {array} \]
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.540 |
|
| \(12\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \end {array} \]
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.187 |
|
| \(13\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.385 |
|
| \(14\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \end {array} \]
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.404 |
|
| \(15\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \end {array} \]
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
2.293 |
|
| \(16\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.104 |
|
| \(17\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{z^{3}}&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.056 |
|
| \(18\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.079 |
|
| \(19\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.108 |
|
| \(20\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }-\left (2 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.074 |
|
| \(21\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.169 |
|
| \(22\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=x^{{3}/{2}} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.095 |
|
| \(23\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=\sqrt {x} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.110 |
|
| \(24\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.090 |
|
| \(25\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.069 |
|
| \(26\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.029 |
|
| \(27\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.027 |
|
| \(28\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.065 |
|
| \(29\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
2.277 |
|
| \(30\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[_linear] |
✗ |
✓ |
✗ |
0.365 |
|
| \(31\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.121 |
|
| \(32\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.085 |
|
| \(33\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.280 |
|
| \(34\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.358 |
|
| \(35\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+\lambda y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.456 |
|
| \(36\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.230 |
|
| \(37\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.585 |
|
| \(38\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.806 |
|
| \(39\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }&=y \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.419 |
|
| \(40\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.759 |
|
| \(41\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.911 |
|
| \(42\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.664 |
|
| \(43\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.717 |
|
| \(44\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
1.708 |
|
| \(45\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.082 |
|
| \(46\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.079 |
|
| \(47\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.078 |
|
| \(48\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.078 |
|
| \(49\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
2.107 |
|
| \(50\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.552 |
|
| \(51\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.660 |
|
| \(52\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.473 |
|
| \(53\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
1.527 |
|
| \(54\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.680 |
|
| \(55\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.613 |
|
| \(56\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+x +1 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.622 |
|
| \(57\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.620 |
|
| \(58\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.645 |
|
| \(59\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right )+\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.666 |
|
| \(60\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=1 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.590 |
|
| \(61\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
0.322 |
|
| \(62\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\frac {1}{x^{2}} \end {array} \]
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
0.366 |
|
| \(63\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[_quadrature] |
✗ |
✓ |
✗ |
0.213 |
|
| \(64\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _quadrature]] |
✗ |
✓ |
✗ |
0.467 |
|
| \(65\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.661 |
|
| \(66\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.533 |
|
| \(67\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.622 |
|
| \(68\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=0\\ y \left (0\right )&=1\\ \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✗ |
0.247 |
|
| \(69\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.410 |
|
| \(70\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.237 |
|
| \(71\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.350 |
|
| \(72\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.726 |
|
| \(73\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.205 |
|
| \(74\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+x \sin \left (y\right )&=0\\ y \left (0\right )&=\frac {\pi }{2}\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[NONE] |
✓ |
✓ |
✗ |
0.057 |
|
| \(75\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }&=y \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.249 |
|
| \(76\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.217 |
|
| \(77\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.399 |
|
| \(78\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.214 |
|
| \(79\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.344 |
|
| \(80\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.260 |
|
| \(81\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \end {array} \]
Series expansion around \(x=\infty \). |
[_Bessel] |
✗ |
✓ |
✓ |
0.228 |
|
| \(82\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.102 |
|
| \(83\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime } x +y&={\mathrm e}^{x}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.728 |
|
| \(84\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.167 |
|
| \(85\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y x&=0 \end {array} \]
Series expansion around \(x=\infty \). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
0.113 |
|
| \(86\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }&=t x+1\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Series expansion around \(t=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
1.011 |
|
| \(87\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.343 |
|
| \(88\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.329 |
|
| \(89\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.772 |
|
| \(90\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.367 |
|
| \(91\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.049 |
|
| \(92\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x -y&=-\ln \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.042 |
|
| \(93\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }+y^{\prime \prime } x +2 y^{\prime }+y x&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-1\\ \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(94\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.344 |
|
| \(95\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.246 |
|
| \(96\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.405 |
|
| \(97\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-\sin \left (x \right ) y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.081 |
|
| \(98\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.087 |
|
| \(99\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 x^{2} y^{\prime }+2 y x&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(100\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }+2 y^{\prime }-x^{3} y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(101\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(102\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(103\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.471 |
|
| \(104\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.861 |
|
| \(105\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }-\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.357 |
|
| \(106\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.030 |
|
| \(107\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.027 |
|
| \(108\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.026 |
|
| \(109\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime }+\frac {x^{2} y^{\prime \prime }}{x +1}-\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.031 |
|
| \(110\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{x +1}+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.029 |
|
| \(111\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.175 |
|
| \(112\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \end {array} \]
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.266 |
|
| \(113\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime } x +\left (x -2\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.023 |
|
| \(114\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime \prime }&=z w \end {array} \]
Series expansion around \(z=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.021 |
|
| \(115\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{2} w^{\prime \prime }+\left (1+z \right ) w^{\prime }-a w&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.388 |
|
| \(116\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{3} \left (1+z \right ) w^{\prime \prime }+z \left (1+2 z \right ) w^{\prime }-\left (1+2 z \right ) w&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.174 |
|