\[ a^2 \left (-y'(x)\right )-e^{2 a x} \sin ^2(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 1.57547 (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 = 0.15 (sec), leaf count = 122
\[\left \{y \left (x \right ) = \frac {108 \left (a^{2}+4\right ) \left (a^{2}+1\right ) \left (-c_{1} {\mathrm e}^{-a x}+c_{2} {\mathrm e}^{a x}+c_{3} a \right ) \left (a^{2}+\frac {4}{9}\right ) a^{2}+\left (9 a^{6}+49 a^{4}+56 a^{2}+\left (-9 a^{6}+36 a^{4}\right ) \cos \left (2 x \right )+\left (-33 a^{5}+12 a^{3}\right ) \sin \left (2 x \right )+16\right ) {\mathrm e}^{2 a x}}{108 a^{9}+588 a^{7}+672 a^{5}+192 a^{3}}\right \}\]