\[ y(x) \left (a^4 \sin ^4(x)-3\right )+y^{(4)}(x) \sin ^4(x)+2 y^{(3)}(x) \sin ^3(x) \cos (x)+\left (\sin ^2(x)-3\right ) \sin ^2(x) y''(x)+\left (2 \sin ^2(x)+3\right ) \sin (x) \cos (x) y'(x)=0 \] ✗ Mathematica : cpu = 0.201916 (sec), leaf count = 0 , could not solve
DSolve[(-3 + a^4*Sin[x]^4)*y[x] + Cos[x]*Sin[x]*(3 + 2*Sin[x]^2)*Derivative[1][y][x] + Sin[x]^2*(-3 + Sin[x]^2)*Derivative[2][y][x] + 2*Cos[x]*Sin[x]^3*Derivative[3][y][x] + Sin[x]^4*Derivative[4][y][x] == 0, y[x], x]
✓ Maple : cpu = 1. (sec), leaf count = 345
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( x \right ) {\mbox {$_2$F$_1$}({\frac {3}{4}}-{\frac {1}{4}\sqrt {-i \left ( -4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }},{\frac {3}{4}}+{\frac {1}{4}\sqrt {-i \left ( -4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}+{\it \_C2}\,\sin \left ( x \right ) {\mbox {$_2$F$_1$}({\frac {3}{4}}+{\frac {1}{4}\sqrt {-i \left ( 4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }},{\frac {3}{4}}-{\frac {1}{4}\sqrt {-i \left ( 4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}+{\it \_C3}\,\sin \left ( x \right ) \cos \left ( x \right ) {\mbox {$_2$F$_1$}({\frac {5}{4}}+{\frac {1}{4}\sqrt {-i \left ( -4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }},{\frac {5}{4}}-{\frac {1}{4}\sqrt {-i \left ( -4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}+{\it \_C4}\,\sin \left ( x \right ) \cos \left ( x \right ) {\mbox {$_2$F$_1$}({\frac {5}{4}}+{\frac {1}{4}\sqrt {-i \left ( 4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }},{\frac {5}{4}}-{\frac {1}{4}\sqrt {-i \left ( 4\,\sqrt {a+i}\sqrt {a-i}\sqrt {a+1}\sqrt {a-1}+5\,i \right ) }};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})} \right \} \]