| # |
ODE |
solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.471 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+9 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
4 y^{\prime \prime } x +8 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| \begin{align*}
x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.111 |
|
| \begin{align*}
y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime } x +\left (5-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3 x +5\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.621 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (6+2 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.314 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.351 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.902 |
|
| \begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.626 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.712 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.233 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \begin{align*}
2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (-9 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.482 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (9-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.968 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| \begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.648 |
|
| \begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.508 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.402 |
|
| \begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.238 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.482 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.794 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.060 |
|
| \begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| \begin{align*}
x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.014 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.959 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.834 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.589 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.676 |
|
| \begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| \begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.679 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.975 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.295 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.883 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.854 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.156 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.566 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.526 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.482 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }-y&=x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.653 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }-y&=x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.622 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.666 |
|
| \begin{align*}
\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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.545 |
|
| \begin{align*}
z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.136 |
|
| \begin{align*}
4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.218 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.959 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.403 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.603 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.981 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.266 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{\prime \prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.660 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.205 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.202 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.651 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.214 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.048 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.321 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.649 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }-\frac {y}{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| \begin{align*}
y^{\prime \prime }-\frac {3 y^{\prime }}{x \left (1-x \right )}+\frac {2 y}{x \left (1-x \right )}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x \left (x +1\right )}-\frac {y}{x \left (x +1\right )}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.591 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| \begin{align*}
y^{\prime \prime } x -2 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.400 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.554 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+a^{3} x^{2} y&=2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.483 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.275 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.133 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.868 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.600 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.742 |
|
| \begin{align*}
4 \left (1-x \right ) x y^{\prime \prime }-4 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.689 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y&=3 x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.658 |
|
| \begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.064 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.538 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
8.275 |
|
| \begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.611 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.746 |
|
| \begin{align*}
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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.900 |
|
| \begin{align*}
\left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| \begin{align*}
\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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| \begin{align*}
-y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.821 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.927 |
|
| \begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.699 |
|
| \begin{align*}
y^{\prime \prime } x +x^{3} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.393 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime } x -{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
y^{\prime \prime } x +x^{5} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.151 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.623 |
|
| \begin{align*}
x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.781 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| \begin{align*}
\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.673 |
|
| \begin{align*}
x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.451 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.632 |
|
| \begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.526 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.272 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.195 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.228 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.102 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.580 |
|
| \begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.561 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.431 |
|
| \begin{align*}
y^{\prime \prime } x +2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.574 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.973 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \begin{align*}
3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.516 |
|
| \begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.682 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{4 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.563 |
|
| \begin{align*}
y^{\prime \prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.206 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 \,{\mathrm e}^{x} y^{\prime } x +3 \cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.200 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (-x^{3}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.128 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.376 |
|
| \begin{align*}
\left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.832 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.607 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.154 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.866 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.140 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.680 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime \prime } x -4 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.204 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.898 |
|
| \begin{align*}
\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.240 |
|
| \begin{align*}
x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.996 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.140 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.914 |
|
| \begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.731 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.529 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
6.220 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \begin{align*}
-\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✗ |
1.636 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.499 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3 x +4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
y^{\prime \prime } x -2 \left (2+x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.570 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| \begin{align*}
x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.583 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.813 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.138 |
|
| \begin{align*}
2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.171 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.555 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.144 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.286 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.500 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
5.468 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.955 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.065 |
|
| \begin{align*}
y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.343 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.185 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.338 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime } x +\left (x^{4}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.635 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.261 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.321 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.368 |
|
| \begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.390 |
|
| \begin{align*}
\left (x +3\right ) y-2 x \left (2+x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.257 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.972 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.436 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.869 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.764 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.936 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.343 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.510 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.531 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| \begin{align*}
2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.127 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.489 |
|
| \begin{align*}
-y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.154 |
|
| \begin{align*}
\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
2.855 |
|
| \begin{align*}
\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{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.718 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.902 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.621 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.012 |
|
| \begin{align*}
y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.361 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.773 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.625 |
|
| \begin{align*}
\left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.038 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.889 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \begin{align*}
x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
5.806 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.277 |
|
| \begin{align*}
t x^{\prime \prime }&=x \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
4.543 |
|
| \begin{align*}
t x^{\prime \prime }&=x^{\prime } \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
4 t^{2} x^{\prime \prime }+4 t x^{\prime }-x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
6.177 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.893 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| \begin{align*}
x \left (x -1\right )^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.695 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.970 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.280 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.234 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.092 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
2 \left (1-x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x -3-\left (x -1\right )^{2} {\mathrm e}^{x}\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
2.819 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.266 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.690 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
2.560 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.397 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.405 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
y^{\prime \prime } x -3 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.986 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| \begin{align*}
U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\
\end{align*} Series expansion around \(r=0\). |
✓ |
✓ |
✓ |
✗ |
0.765 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=5 \sqrt {x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.836 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=2 x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.819 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.712 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (3 x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (2 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.326 |
|
| \begin{align*}
\left (x +3\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.593 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.684 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.502 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
3.381 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.024 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +\left (3-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.353 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.224 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (2 x -3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.222 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
5.220 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
4.264 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t +t^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t -a \,t^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| \begin{align*}
t y^{\prime \prime }-4 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.194 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
4.045 |
|