\[ y''(x)=\left (3 \sin ^2(x)+1\right ) \csc (x) \sec (x) y'(x)+y(x) \tan ^2(x) \] ✓ Mathematica : cpu = 0.293085 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_1 \cos ^{\frac {\sqrt {13}}{2}-\frac {3}{2}}(x)+c_2 \cos ^{-\frac {3}{2}-\frac {\sqrt {13}}{2}}(x)\right \}\right \}\] ✓ Maple : cpu = 0.184 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \cos \left ( x \right ) \right ) ^{-{\frac {3}{2}}+{\frac {\sqrt {13}}{2}}}+{\it \_C2}\, \left ( \cos \left ( x \right ) \right ) ^{-{\frac {3}{2}}-{\frac {\sqrt {13}}{2}}} \right \} \]