\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -{a}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{{\rm e}^{2\,ax}} \left ( \sin \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.593075 (sec), leaf count = 128 \[ \left \{\left \{y(x)\to \frac {e^{-a x} \left (-9 \left (a^2-4\right ) a^4 e^{3 a x} \cos (2 x)-3 \left (11 a^2-4\right ) a^3 e^{3 a x} \sin (2 x)+\left (9 a^6+49 a^4+56 a^2+16\right ) \left (12 a^2 c_1 e^{2 a x}-12 a^2 c_2+e^{3 a x}\right )\right )}{12 a^3 \left (9 a^6+49 a^4+56 a^2+16\right )}+c_3\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 230 \[ \left \{ y \left ( x \right ) ={\frac {108\,{{\rm e}^{ax}}{\it \_C2}\,{a }^{8}-108\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{8}+108\,{\it \_C3}\,{a}^{9} -9\,{a}^{6}{{\rm e}^{2\,ax}}\cos \left ( 2\,x \right ) +588\,{{\rm e}^{a x}}{\it \_C2}\,{a}^{6}-588\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{6}+588\,{ \it \_C3}\,{a}^{7}-33\,{{\rm e}^{2\,ax}}\sin \left ( 2\,x \right ) {a}^{ 5}+9\,{{\rm e}^{2\,ax}}{a}^{6}+36\,{{\rm e}^{2\,ax}}\cos \left ( 2\,x \right ) {a}^{4}+672\,{{\rm e}^{ax}}{\it \_C2}\,{a}^{4}-672\,{{\rm e}^ {-ax}}{\it \_C1}\,{a}^{4}+672\,{\it \_C3}\,{a}^{5}+12\,{{\rm e}^{2\,ax }}\sin \left ( 2\,x \right ) {a}^{3}+49\,{{\rm e}^{2\,ax}}{a}^{4}+192\,{ {\rm e}^{ax}}{\it \_C2}\,{a}^{2}-192\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{ 2}+192\,{\it \_C3}\,{a}^{3}+56\,{{\rm e}^{2\,ax}}{a}^{2}+16\,{{\rm e}^ {2\,ax}}}{108\,{a}^{9}+588\,{a}^{7}+672\,{a}^{5}+192\,{a}^{3}}} \right \} \]