\[ a^2 \left (-y'(x)\right )-e^{2 a x} \sin ^2(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 1.02056 (sec), leaf count = 128
\[\left \{\left \{y(x)\to \frac {e^{-a x} \left (-3 \left (11 a^2-4\right ) a^3 e^{3 a x} \sin (2 x)-9 \left (a^2-4\right ) a^4 e^{3 a x} \cos (2 x)+\left (9 a^6+49 a^4+56 a^2+16\right ) \left (12 a^2 c_1 e^{2 a x}-12 a^2 c_2+e^{3 a x}\right )\right )}{12 a^3 \left (9 a^6+49 a^4+56 a^2+16\right )}+c_3\right \}\right \}\] ✓ Maple : cpu = 0.249 (sec), leaf count = 122
\[ \left \{ y \left ( x \right ) ={\frac {1}{108\,{a}^{9}+588\,{a}^{7}+672\,{a}^{5}+192\,{a}^{3}} \left ( \left ( \left ( -9\,{a}^{6}+36\,{a}^{4} \right ) \cos \left ( 2\,x \right ) + \left ( -33\,{a}^{5}+12\,{a}^{3} \right ) \sin \left ( 2\,x \right ) +9\,{a}^{6}+49\,{a}^{4}+56\,{a}^{2}+16 \right ) {{\rm e}^{2\,ax}}+108\,{a}^{2} \left ( a{\it \_C3}-{{\rm e}^{-ax}}{\it \_C1}+{{\rm e}^{ax}}{\it \_C2} \right ) \left ( {a}^{2}+4/9 \right ) \left ( {a}^{2}+4 \right ) \left ( {a}^{2}+1 \right ) \right ) } \right \} \]