\[ a^2 \left (-y'(x)\right )-e^{2 a x} \sin ^2(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.614525 (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 = 0.133 (sec), leaf count = 230
\[ \left \{ y \left ( x \right ) ={\frac {108\,{{\rm e}^{ax}}{\it \_C2}\,{a}^{8}-108\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{8}+108\,{\it \_C3}\,{a}^{9}-9\,{a}^{6}{{\rm e}^{2\,ax}}\cos \left ( 2\,x \right ) +588\,{{\rm e}^{ax}}{\it \_C2}\,{a}^{6}-588\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{6}+588\,{\it \_C3}\,{a}^{7}-33\,{{\rm e}^{2\,ax}}\sin \left ( 2\,x \right ) {a}^{5}+9\,{{\rm e}^{2\,ax}}{a}^{6}+36\,{{\rm e}^{2\,ax}}\cos \left ( 2\,x \right ) {a}^{4}+672\,{{\rm e}^{ax}}{\it \_C2}\,{a}^{4}-672\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{4}+672\,{\it \_C3}\,{a}^{5}+12\,{{\rm e}^{2\,ax}}\sin \left ( 2\,x \right ) {a}^{3}+49\,{{\rm e}^{2\,ax}}{a}^{4}+192\,{{\rm e}^{ax}}{\it \_C2}\,{a}^{2}-192\,{{\rm e}^{-ax}}{\it \_C1}\,{a}^{2}+192\,{\it \_C3}\,{a}^{3}+56\,{{\rm e}^{2\,ax}}{a}^{2}+16\,{{\rm e}^{2\,ax}}}{108\,{a}^{9}+588\,{a}^{7}+672\,{a}^{5}+192\,{a}^{3}}} \right \} \]