\[ \boxed { {x}^{4}{\it d4y} \left ( x \right ) +6\,{x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( 4\,{x}^{4}+ \left ( -2\,{\mu }^{2}-2\,{\nu }^{2}+7 \right ) {x}^{2} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 16\,{x}^{3}+ \left ( -2\,{\mu }^{2}-2\,{\nu }^{2}+1 \right ) x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 8\,{x}^{2}+ \left ( {\mu }^{2}-{\nu }^{2} \right ) ^{2} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.620079 (sec), leaf count = 238 \[ \left \{\left \{y(x)\to c_1 x^{-\mu -\nu } \, _2F_3\left (-\frac {\mu }{2}-\frac {\nu }{2}+\frac {1}{2},-\frac {\mu }{2}-\frac {\nu }{2}+1;1-\mu ,1-\nu ,-\mu -\nu +1;-x^2\right )+c_2 x^{\mu -\nu } \, _2F_3\left (\frac {\mu }{2}-\frac {\nu }{2}+\frac {1}{2},\frac {\mu }{2}-\frac {\nu }{2}+1;\mu +1,1-\nu ,\mu -\nu +1;-x^2\right )+c_3 x^{\nu -\mu } \, _2F_3\left (-\frac {\mu }{2}+\frac {\nu }{2}+\frac {1}{2},-\frac {\mu }{2}+\frac {\nu }{2}+1;1-\mu ,\nu +1,-\mu +\nu +1;-x^2\right )+c_4 x^{\mu +\nu } \, _2F_3\left (\frac {\mu }{2}+\frac {\nu }{2}+\frac {1}{2},\frac {\mu }{2}+\frac {\nu }{2}+1;\mu +1,\nu +1,\mu +\nu +1;-x^2\right )\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{\nu }\left (x\right )} {{\sl J}_{\mu }\left (x\right )}+{\it \_C2}\,{{\sl J}_{\nu }\left (x \right )}{{\sl Y}_{\mu }\left (x\right )}+{\it \_C3}\,{{\sl Y}_{\nu }\left ( x\right )}{{\sl J}_{\mu }\left (x\right )}+{\it \_C4}\,{{\sl Y}_{\nu }\left (x\right )}{{\sl Y}_{\mu }\left (x\right )} \right \} \]