\[ \left (x \left (-2 \mu ^2-2 \nu ^2+1\right )+16 x^3\right ) y'(x)+y(x) \left (\left (\mu ^2-\nu ^2\right )^2+8 x^2\right )+\left (x^2 \left (-2 \mu ^2-2 \nu ^2+7\right )+4 x^4\right ) y''(x)+x^4 y^{(4)}(x)+6 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.642096 (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 = 0.389 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{\nu }\left (x\right )}{{\sl J}_{\mu }\left (x\right )}+{\it \_C2}\,{{\sl J}_{\nu }\left (x\right )}{{\sl Y}_{\mu }\left (x\right )}+{\it \_C3}\,{{\sl Y}_{\nu }\left (x\right )}{{\sl J}_{\mu }\left (x\right )}+{\it \_C4}\,{{\sl Y}_{\nu }\left (x\right )}{{\sl Y}_{\mu }\left (x\right )} \right \} \]