\[ \left (-2 \left (x^2-1\right ) (\mu (\mu +1)+\nu (\nu +1))+24 x^3-8\right ) y''(x)-6 x (\mu (\mu +1)+\nu (\nu +1)-2) y'(x)+\left ((\mu (\mu +1)-\nu (\nu +1))^2-2 \mu (\mu +1)-2 \nu (\nu +1)\right ) y(x)+\left (x^2-1\right )^2 y^{(4)}(x)+10 x \left (x^2-1\right ) y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 95.3641 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\mu -\nu -1) (\mu -\nu +1) (\mu +\nu ) (\mu +\nu +2) \unicode {f818}(\unicode {f817})-6 \unicode {f817} \left (\mu ^2+\mu +\nu ^2+\nu -2\right ) \unicode {f818}'(\unicode {f817})-2 \left (-12 \unicode {f817}^3+\mu ^2 \unicode {f817}^2+\nu ^2 \unicode {f817}^2+\mu \unicode {f817}^2+\nu \unicode {f817}^2-\mu ^2-\nu ^2-\mu -\nu +4\right ) \unicode {f818}''(\unicode {f817})+\left (10 \unicode {f817}^3-10 \unicode {f817}\right ) \unicode {f818}^{(3)}(\unicode {f817})+\left (\unicode {f817}^4-2 \unicode {f817}^2+1\right ) \unicode {f818}^{(4)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.563 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) = \left ( {\it LegendreQ} \left ( \mu ,x \right ) {\it \_C2}+{\it \_C1}\,{\it LegendreP} \left ( \mu ,x \right ) \right ) {\it LegendreP} \left ( \nu ,x \right ) +{\it LegendreQ} \left ( \nu ,x \right ) \left ( {\it LegendreQ} \left ( \mu ,x \right ) {\it \_C4}+{\it \_C3}\,{\it LegendreP} \left ( \mu ,x \right ) \right ) \right \} \]