\[ y''(x)=-4 y(x) \sin (3 x) \csc ^3(x) \] ✓ Mathematica : cpu = 0.151365 (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 = 0.159 (sec), leaf count = 38
\[\left \{y \left (x \right ) = \left (c_{1} \LegendreP \left (-\frac {1}{2}+4 i, \frac {i \sqrt {47}}{2}, \cos \left (x \right )\right )+c_{2} \LegendreQ \left (-\frac {1}{2}+4 i, \frac {i \sqrt {47}}{2}, \cos \left (x \right )\right )\right ) \left (\sqrt {\sin }\left (x \right )\right )\right \}\]