\[ \boxed { \left ( {x}^{2}-1 \right ) ^{2}{\it d4y} \left ( x \right ) +10\,x \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( 24\,{x}^{2}-8-2\, \left ( \mu \, \left ( \mu +1 \right ) +\nu \, \left ( \nu +1 \right ) \right ) \left ( {x}^{2}-1 \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -6\,x \left ( \mu \, \left ( \mu +1 \right ) +\nu \, \left ( \nu +1 \right ) -2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( \left ( \mu \, \left ( \mu +1 \right ) -\nu \, \left ( \nu +1 \right ) \right ) ^{2}-2\,\mu \, \left ( \mu +1 \right ) -2\,\nu \, \left ( \nu +1 \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 93.272844 (sec), leaf count = 174 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\mu -\nu -1) (\mu -\nu +1) (\mu +\nu ) (\mu +\nu +2) \unicode {f818}(\unicode {f817})-6 \unicode {f817} \left (\mu ^2+\mu +\nu ^2+\nu -2\right ) \unicode {f818}'(\unicode {f817})-2 \left (-12 \unicode {f817}^3+\mu ^2 \unicode {f817}^2+\nu ^2 \unicode {f817}^2+\mu \unicode {f817}^2+\nu \unicode {f817}^2-\mu ^2-\nu ^2-\mu -\nu +4\right ) \unicode {f818}''(\unicode {f817})+\left (10 \unicode {f817}^3-10 \unicode {f817}\right ) \unicode {f818}^{(3)}(\unicode {f817})+\left (\unicode {f817}^4-2 \unicode {f817}^2+1\right ) \unicode {f818}^{(4)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3,\unicode {f818}^{(3)}(0)=c_4\right \},\langle \langle \rangle \rangle \right )(x)\right \}\right \} \]
Maple: cpu = 0.203 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( \nu ,x \right ) {\it LegendreP} \left ( \mu ,x \right ) +{\it \_C2}\,{\it LegendreP} \left ( \nu ,x \right ) {\it LegendreQ} \left ( \mu ,x \right ) + {\it \_C3}\,{\it LegendreQ} \left ( \nu ,x \right ) {\it LegendreP} \left ( \mu ,x \right ) +{\it \_C4}\,{\it LegendreQ} \left ( \nu ,x \right ) {\it LegendreQ} \left ( \mu ,x \right ) \right \} \]