| # |
ODE |
solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
2 y^{\prime \prime } x +3 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
2 y^{\prime \prime } x -y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
3 y^{\prime \prime } x +2 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (-2 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+2 y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.475 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.891 |
|
| \begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (2 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.720 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \begin{align*}
18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \begin{align*}
x \left (x^{2}+x +3\right ) y^{\prime \prime }+\left (-x^{2}+x +4\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x -\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.612 |
|
| \begin{align*}
x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
3 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+5 x \left (x^{2}+1\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.595 |
|
| \begin{align*}
8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
9 x^{2} \left (x +5\right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| \begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.858 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). | ✓ | ✓ | ✓ | ✓ | 0.655 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| \begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.584 |
|
| \begin{align*}
t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.978 |
|
| \begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
31.342 |
|
| \begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.077 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
4 \left (1-x \right ) x^{2} y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.829 |
|
| \begin{align*}
2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (x^{3}+1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \begin{align*}
3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=-x^{3}+x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.151 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.970 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=x^{3}+1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.987 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=x \left (x^{2}+x +1\right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| \begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=x^{2} \left (x +1\right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.187 |
|
| \begin{align*}
4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (z +1\right ) y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.553 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.643 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (x +5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.695 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (3 x +7\right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 \,{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {3 y^{\prime } x}{2}-\frac {\left (x +1\right ) y}{2}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
y^{\prime \prime }-\frac {\left (-3 x^{2}+x \right ) y^{\prime }}{2 x^{3}+2 x^{2}}+\frac {y}{2 x^{3}+2 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| \begin{align*}
\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (1-n \right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (1-n \right ) x y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.869 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \begin{align*}
2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.896 |
|
| \begin{align*}
2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 \left (x +a \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.886 |
|
| \begin{align*}
2 y^{\prime \prime } x -y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
y^{\prime \prime } x +\left (\frac {1}{2}-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.578 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| \begin{align*}
x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ | 1.164 |
|
| \begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
3 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| \begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.809 |
|
| \begin{align*}
4 y^{\prime \prime } x +y^{\prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-6\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.641 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| \begin{align*}
\left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (2+x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.982 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.247 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| \begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.601 |
|
| \begin{align*}
3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-1\). | ✓ | ✓ | ✓ | ✗ | 0.593 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| \begin{align*}
\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.196 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✗ |
1.191 |
|
| \begin{align*}
p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \begin{align*}
x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.500 |
|
| \begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
3 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
2 \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| \begin{align*}
x \left (4-x \right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }-5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
-y x -\left (2 x^{2}+1\right ) y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.609 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \begin{align*}
2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.035 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (4 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.598 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.579 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.624 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{4} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.569 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=x^{2}+2 x \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ | 0.743 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.556 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{3}+\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.712 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) x^{3} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) x^{3}+\sin \left (x \right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.738 |
|
| \begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.522 |
|
| \begin{align*}
\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (2 x^{2}+\frac {5}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.552 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \begin{align*}
3 y^{\prime \prime } x -\left (x -2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.759 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }-k y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.805 |
|
| \begin{align*}
2 y^{\prime \prime } x -5 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
9 y^{\prime \prime } x +14 y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
7 y^{\prime \prime } x +10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ | 0.800 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
3 y^{\prime \prime } x +11 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
9 \left (1-x \right ) x y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.267 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.368 |
|
| \begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
2.139 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.575 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (x +1\right ) y}{2 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.814 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.638 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.097 |
|
| \begin{align*}
18 x^{2} y^{\prime \prime }+3 x \left (x +5\right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.047 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.619 |
|
| \begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (1+3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.148 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.623 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.964 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.830 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (-n^{2}+x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
-6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.247 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.673 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{16}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {2}{3}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.795 |
|
| \begin{align*}
2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{4}-4 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.488 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| \begin{align*}
25 x^{2} y^{\prime \prime }+\left (4+2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
2 t y^{\prime \prime }+y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1-t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
t y^{\prime \prime }+2 \left (i t -k \right ) y^{\prime }-2 i k y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|