\[ \left (x \left (-2 \mu ^2-2 \nu ^2+1\right )+16 x^3\right ) y'(x)+y(x) \left (\left (\mu ^2-\nu ^2\right )^2+8 x^2\right )+\left (x^2 \left (-2 \mu ^2-2 \nu ^2+7\right )+4 x^4\right ) y''(x)+x^4 y^{(4)}(x)+6 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.448934 (sec), leaf count = 238
DSolve[((mu^2 - nu^2)^2 + 8*x^2)*y[x] + ((1 - 2*mu^2 - 2*nu^2)*x + 16*x^3)*Derivative[1][y][x] + ((7 - 2*mu^2 - 2*nu^2)*x^2 + 4*x^4)*Derivative[2][y][x] + 6*x^3*Derivative[3][y][x] + x^4*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 x^{-\mu -\nu } \, _2F_3\left (-\frac {\mu }{2}-\frac {\nu }{2}+\frac {1}{2},-\frac {\mu }{2}-\frac {\nu }{2}+1;1-\mu ,1-\nu ,-\mu -\nu +1;-x^2\right )+c_2 x^{\mu -\nu } \, _2F_3\left (\frac {\mu }{2}-\frac {\nu }{2}+\frac {1}{2},\frac {\mu }{2}-\frac {\nu }{2}+1;\mu +1,1-\nu ,\mu -\nu +1;-x^2\right )+c_3 x^{\nu -\mu } \, _2F_3\left (-\frac {\mu }{2}+\frac {\nu }{2}+\frac {1}{2},-\frac {\mu }{2}+\frac {\nu }{2}+1;1-\mu ,\nu +1,-\mu +\nu +1;-x^2\right )+c_4 x^{\mu +\nu } \, _2F_3\left (\frac {\mu }{2}+\frac {\nu }{2}+\frac {1}{2},\frac {\mu }{2}+\frac {\nu }{2}+1;\mu +1,\nu +1,\mu +\nu +1;-x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.272 (sec), leaf count = 35
dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+(4*x^4+(-2*mu^2-2*nu^2+7)*x^2)*diff(diff(y(x),x),x)+(16*x^3+(-2*mu^2-2*nu^2+1)*x)*diff(y(x),x)+(8*x^2+(mu^2-nu^2)^2)*y(x)=0,y(x))
\[y \left (x \right ) = \left (\BesselY \left (\mu , x\right ) c_{2}+c_{1} \BesselJ \left (\mu , x\right )\right ) \BesselJ \left (\nu , x\right )+\BesselY \left (\nu , x\right ) \left (\BesselY \left (\mu , x\right ) c_{4}+c_{3} \BesselJ \left (\mu , x\right )\right )\]