\[ \left (-2 \left (x^2-1\right ) (\mu (\mu +1)+\nu (\nu +1))+24 x^3-8\right ) y''(x)-6 x (\mu (\mu +1)+\nu (\nu +1)-2) y'(x)+\left ((\mu (\mu +1)-\nu (\nu +1))^2-2 \mu (\mu +1)-2 \nu (\nu +1)\right ) y(x)+\left (x^2-1\right )^2 y^{(4)}(x)+10 x \left (x^2-1\right ) y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 86.1436 (sec), leaf count = 0
, DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
✓ Maple : cpu = 0.345 (sec), leaf count = 35
\[y \relax (x ) = \left (\LegendreQ \left (\mu , x\right ) c_{2}+c_{1} \LegendreP \left (\mu , x\right )\right ) \LegendreP \left (\nu , x\right )+\LegendreQ \left (\nu , x\right ) \left (\LegendreQ \left (\mu , x\right ) c_{4}+c_{3} \LegendreP \left (\mu , x\right )\right )\]