\[ y(x) \left (a^4 \sin ^4(x)-3\right )+y^{(4)}(x) \sin ^4(x)+2 y^{(3)}(x) \sin ^3(x) \cos (x)+\left (\sin ^2(x)-3\right ) \sin ^2(x) y''(x)+\left (2 \sin ^2(x)+3\right ) \sin (x) \cos (x) y'(x)=0 \] ✗ Mathematica : cpu = 0.22893 (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 = 1.019 (sec), leaf count = 252
\[ \left \{ y \left ( x \right ) = \left ( {\mbox {$_2$F$_1$}({\frac {3}{4}}-{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {3}{4}}+{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C1}+{\mbox {$_2$F$_1$}({\frac {3}{4}}+{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {3}{4}}-{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C2}+\cos \left ( x \right ) \left ( {\mbox {$_2$F$_1$}({\frac {5}{4}}-{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {5}{4}}+{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C3}+{\mbox {$_2$F$_1$}({\frac {5}{4}}+{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {5}{4}}-{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C4} \right ) \right ) \sin \left ( x \right ) \right \} \]