| # |
ODE |
solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+9 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }-4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime } x +8 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.484 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (3-x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (5-x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (3 x +5\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x -\left (6+2 x \right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.519 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
22.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
22.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
22.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.940 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.886 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.843 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.889 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.743 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.984 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (9-x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.004 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.931 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.096 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
5.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.667 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.249 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
5.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.974 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.988 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.117 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.538 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
9.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
2.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
7.322 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
7.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+y^{\prime } t +2 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
4.757 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
9.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
5.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
9.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.418 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.390 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.280 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
1.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
11.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
8.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+y^{\prime } t +2 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
7.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
8.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
7.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.394 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
8.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +3 y^{\prime }-y&=x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
6.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +3 y^{\prime }-y&=x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
6.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
6.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.864 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.146 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x +2\right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }-\frac {y}{x}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {3 y^{\prime }}{x \left (1-x \right )}+\frac {2 y}{x \left (1-x \right )}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {\left (-1+x \right ) y^{\prime }}{x \left (x +1\right )}-\frac {y}{x \left (x +1\right )}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -2 y^{\prime } x -y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+a^{3} x^{2} y&=2 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.667 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+x \right ) y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.150 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 \left (1-x \right ) x y^{\prime \prime }-4 y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=3 x^{2} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.373 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.991 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -2 y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3-x \right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.286 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.249 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +x^{3} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime } x -{\mathrm e}^{x} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +x^{5} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.320 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
14.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.609 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.190 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.159 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.285 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
12.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +3 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.785 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
10.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
7.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.236 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +5 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
5.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.414 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{4 x}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
14.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 \,{\mathrm e}^{x} y^{\prime } x +3 \cos \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
18.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (-x^{3}+3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.149 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
16.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
18.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
11.861 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
16.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
28.932 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -4 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.942 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
17.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
28.826 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
16.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
15.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
24.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.322 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.196 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
12.236 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
19.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x +3\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \end {array} \]
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✗ |
4.426 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
14.879 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (3 x +4\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -2 \left (2+x \right ) y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
15.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
17.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x \left (-x +2\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
32.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.716 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+8 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.879 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
24.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
32.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
20.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (3-x \right ) y^{\prime }-5 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
31.572 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
27.564 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
22.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime } x +\left (x^{4}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
33.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.937 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.862 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.431 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +3\right ) y-2 x \left (2+x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
21.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.200 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.958 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.716 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.170 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.803 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}-x \right ) y^{\prime \prime }+\left (-2+2 x \right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.194 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +4 y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
15.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.722 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y&=0 \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
30.347 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
36.311 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
27.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.370 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
34.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
26.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
16.598 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y&=0 \end {array} \]
Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
27.251 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
27.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \end {array} \]
Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
24.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
27.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
33.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-1+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.954 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.610 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
10.445 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
7.228 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.178 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }&=x \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
13.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }&=x^{\prime } \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} x^{\prime \prime }+4 t x^{\prime }-x&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+3 t x^{\prime }&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
5.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
13.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right )^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.267 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.954 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
12.966 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (1-x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x -3-\left (-1+x \right )^{2} {\mathrm e}^{x}\right ) y&=0 \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.722 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
16.095 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \end {array} \]
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
12.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.234 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
16.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
18.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
16.960 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
16.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -3 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \end {array} \]
Series expansion around \(r=0\). |
✓ |
✓ |
✓ |
✗ |
0.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y&=5 \sqrt {x} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=2 x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-9\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (3 x^{2}-4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (2 x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (2+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
17.325 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +3\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.574 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
18.932 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
10.696 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \end {array} \]
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
17.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
10.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +\left (3-2 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }-3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (2 x -3\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.417 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t +t^{2} y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.912 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -a \,t^{2} y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
13.860 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-4 y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
8.791 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.278 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+3 x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -2 y^{\prime } x +2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-9\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.278 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2 x +2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime } x -y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.166 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{2} w^{\prime \prime }+w^{\prime } z +\left (z^{2}-4\right ) w&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
3.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z \left (1-z \right ) w^{\prime \prime }-\left (1+z \right ) w^{\prime }+w&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z w^{\prime \prime }&=w \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
5.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{2} \left (1-z \right )^{2} w^{\prime \prime }+z \left (1-z \right ) \left (1-2 z \right ) w^{\prime }-w&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (2-z \right ) z^{2} w^{\prime \prime }-\left (4-z \right ) z w^{\prime }+\left (3-z \right ) w&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✗ |
0.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{2} w^{\prime \prime }-\left (k \,z^{2}+5 z \right ) w^{\prime }+\left (3 k z +5\right ) w&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✗ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (2 x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime }-12 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z w^{\prime \prime }+\left (a z +2\right ) w^{\prime }+\left (b z +a \right ) w&=0 \end {array} \]
Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
4.397 |
|