\[ y''(x)=-4 y(x) \sin (3 x) \csc ^3(x) \] ✓ Mathematica : cpu = 0.159127 (sec), leaf count = 70
\[\left \{\left \{y(x)\to c_1 \sqrt [4]{\cos ^2(x)-1} P_{-\frac {1}{2}+4 i}^{\frac {i \sqrt {47}}{2}}(\cos (x))+c_2 \sqrt [4]{\cos ^2(x)-1} Q_{-\frac {1}{2}+4 i}^{\frac {i \sqrt {47}}{2}}(\cos (x))\right \}\right \}\]
✓ Maple : cpu = 0.15 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {\sin \left ( x \right ) }{\it LegendreP} \left ( -{\frac {1}{2}}+4\,i,{\frac {i}{2}}\sqrt {47},\cos \left ( x \right ) \right ) +{\it \_C2}\,\sqrt {\sin \left ( x \right ) }{\it LegendreQ} \left ( -{\frac {1}{2}}+4\,i,{\frac {i}{2}}\sqrt {47},\cos \left ( x \right ) \right ) \right \} \]