\[ y'(x) \left (4 \nu (\nu +1) \sin ^2(x)+\cos (2 x)\right )+2 \nu (\nu +1) y(x) \sin (2 x)+3 \sin (x) \cos (x) y''(x)+y^{(3)}(x) \sin ^2(x)=0 \] ✓ Mathematica : cpu = 0.0783715 (sec), leaf count = 35
\[\left \{\left \{y(x)\to c_3 P_{\nu }(\cos (x)) Q_{\nu }(\cos (x))+c_1 P_{\nu }(\cos (x)){}^2+c_2 Q_{\nu }(\cos (x)){}^2\right \}\right \}\] ✓ Maple : cpu = 0.803 (sec), leaf count = 113
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\mbox {$_2$F$_1$}(-{\frac {\nu }{2}},{\frac {\nu }{2}}+{\frac {1}{2}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \right ) ^{2}+{\it \_C2}\, \left ( \cos \left ( 2\,x \right ) +1 \right ) \left ( {\mbox {$_2$F$_1$}({\frac {\nu }{2}}+1,{\frac {1}{2}}-{\frac {\nu }{2}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \right ) ^{2}+{\it \_C3}\,{\mbox {$_2$F$_1$}(-{\frac {\nu }{2}},{\frac {\nu }{2}}+{\frac {1}{2}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})}\sqrt {\cos \left ( 2\,x \right ) +1}{\mbox {$_2$F$_1$}({\frac {\nu }{2}}+1,{\frac {1}{2}}-{\frac {\nu }{2}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \right \} \]