\[ y(x) \left (a^4 \sin ^4(x)-3\right )+\left (2 \sin ^2(x)+3\right ) \sin (x) \cos (x) y'(x)+\left (\sin ^2(x)-3\right ) \sin ^2(x) y''(x)+y^{(4)}(x) \sin ^4(x)+2 y^{(3)}(x) \sin ^3(x) \cos (x)=0 \] ✓ Mathematica : cpu = 0.134194 (sec), leaf count = 270
\[\left \{\left \{y(x)\to c_1 \sin (x) \, _2F_1\left (\frac {1}{4} \left (3-\sqrt {5-4 \sqrt {1-a^4}}\right ),\frac {1}{4} \left (\sqrt {5-4 \sqrt {1-a^4}}+3\right );\frac {1}{2};\cos ^2(x)\right )+c_3 \sin (x) \cos (x) \, _2F_1\left (\frac {1}{4} \left (5-\sqrt {5-4 \sqrt {1-a^4}}\right ),\frac {1}{4} \left (\sqrt {5-4 \sqrt {1-a^4}}+5\right );\frac {3}{2};\cos ^2(x)\right )+c_2 \sin (x) \, _2F_1\left (\frac {1}{4} \left (3-\sqrt {4 \sqrt {1-a^4}+5}\right ),\frac {1}{4} \left (\sqrt {4 \sqrt {1-a^4}+5}+3\right );\frac {1}{2};\cos ^2(x)\right )+c_4 \sin (x) \cos (x) \, _2F_1\left (\frac {1}{4} \left (5-\sqrt {4 \sqrt {1-a^4}+5}\right ),\frac {1}{4} \left (\sqrt {4 \sqrt {1-a^4}+5}+5\right );\frac {3}{2};\cos ^2(x)\right )\right \}\right \}\] ✓ Maple : cpu = 1.268 (sec), leaf count = 252
\[ \left \{ y \left ( x \right ) = \left ( {\mbox {$_2$F$_1$}({\frac {3}{4}}-{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {3}{4}}+{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C1}+{\mbox {$_2$F$_1$}({\frac {3}{4}}+{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {3}{4}}-{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {1}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C2}+\cos \left ( x \right ) \left ( {\mbox {$_2$F$_1$}({\frac {5}{4}}+{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {5}{4}}-{\frac {1}{4}\sqrt {-4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C3}+{\mbox {$_2$F$_1$}({\frac {5}{4}}-{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}},{\frac {5}{4}}+{\frac {1}{4}\sqrt {4\,\sqrt {- \left ( a-1 \right ) \left ( a+1 \right ) \left ( {a}^{2}+1 \right ) }+5}};\,{\frac {3}{2}};\, \left ( \cos \left ( x \right ) \right ) ^{2})}{\it \_C4} \right ) \right ) \sin \left ( x \right ) \right \} \]