\[ y'(x) \left (4 \nu (\nu +1) \sin ^2(x)+\cos (2 x)\right )+2 \nu (\nu +1) y(x) \sin (2 x)+y^{(3)}(x) \sin ^2(x)+3 \sin (x) \cos (x) y''(x)=0 \] ✗ Mathematica : cpu = 0.168492 (sec), leaf count = 0 , could not solve
DSolve[2*nu*(1 + nu)*Sin[2*x]*y[x] + (Cos[2*x] + 4*nu*(1 + nu)*Sin[x]^2)*Derivative[1][y][x] + 3*Cos[x]*Sin[x]*Derivative[2][y][x] + Sin[x]^2*Derivative[3][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.251 (sec), leaf count = 113
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\mbox {$_2$F$_1$}(-{\frac {\nu }{2}},{\frac {\nu }{2}}+{\frac {1}{2}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \right ) ^{2}+{\it \_C2}\, \left ( \cos \left ( 2\,x \right ) +1 \right ) \left ( {\mbox {$_2$F$_1$}(1+{\frac {\nu }{2}},{\frac {1}{2}}-{\frac {\nu }{2}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \right ) ^{2}+{\it \_C3}\,{\mbox {$_2$F$_1$}(-{\frac {\nu }{2}},{\frac {\nu }{2}}+{\frac {1}{2}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})}\sqrt {\cos \left ( 2\,x \right ) +1}{\mbox {$_2$F$_1$}(1+{\frac {\nu }{2}},{\frac {1}{2}}-{\frac {\nu }{2}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \right \} \]