\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +y \left ( x \right ) -\sin \left ( ax \right ) \sin \left ( bx \right ) =0} \]
Mathematica: cpu = 0.532068 (sec), leaf count = 1163 \[ \left \{\left \{y(x)\to c_1 \cos (x)+c_2 \sin (x)+\frac {-\cos (x) \cos ((a-b-1) x) a^3+\cos (x) \cos ((a-b+1) x) a^3+\cos (x) \cos ((a+b-1) x) a^3-\cos (x) \cos ((a+b+1) x) a^3+\sin (x) \sin ((a-b-1) x) a^3+\sin (x) \sin ((a-b+1) x) a^3-\sin (x) \sin ((a+b-1) x) a^3-\sin (x) \sin ((a+b+1) x) a^3-b \cos (x) \cos ((a-b-1) x) a^2-\cos (x) \cos ((a-b-1) x) a^2+b \cos (x) \cos ((a-b+1) x) a^2-\cos (x) \cos ((a-b+1) x) a^2-b \cos (x) \cos ((a+b-1) x) a^2+\cos (x) \cos ((a+b-1) x) a^2+b \cos (x) \cos ((a+b+1) x) a^2+\cos (x) \cos ((a+b+1) x) a^2+b \sin (x) \sin ((a-b-1) x) a^2+\sin (x) \sin ((a-b-1) x) a^2+b \sin (x) \sin ((a-b+1) x) a^2-\sin (x) \sin ((a-b+1) x) a^2+b \sin (x) \sin ((a+b-1) x) a^2-\sin (x) \sin ((a+b-1) x) a^2+b \sin (x) \sin ((a+b+1) x) a^2+\sin (x) \sin ((a+b+1) x) a^2+b^2 \cos (x) \cos ((a-b-1) x) a-2 b \cos (x) \cos ((a-b-1) x) a+\cos (x) \cos ((a-b-1) x) a-b^2 \cos (x) \cos ((a-b+1) x) a-2 b \cos (x) \cos ((a-b+1) x) a-\cos (x) \cos ((a-b+1) x) a-b^2 \cos (x) \cos ((a+b-1) x) a-2 b \cos (x) \cos ((a+b-1) x) a-\cos (x) \cos ((a+b-1) x) a+b^2 \cos (x) \cos ((a+b+1) x) a-2 b \cos (x) \cos ((a+b+1) x) a+\cos (x) \cos ((a+b+1) x) a-b^2 \sin (x) \sin ((a-b-1) x) a+2 b \sin (x) \sin ((a-b-1) x) a-\sin (x) \sin ((a-b-1) x) a-b^2 \sin (x) \sin ((a-b+1) x) a-2 b \sin (x) \sin ((a-b+1) x) a-\sin (x) \sin ((a-b+1) x) a+b^2 \sin (x) \sin ((a+b-1) x) a+2 b \sin (x) \sin ((a+b-1) x) a+\sin (x) \sin ((a+b-1) x) a+b^2 \sin (x) \sin ((a+b+1) x) a-2 b \sin (x) \sin ((a+b+1) x) a+\sin (x) \sin ((a+b+1) x) a+b^3 \cos (x) \cos ((a-b-1) x)-b^2 \cos (x) \cos ((a-b-1) x)-b \cos (x) \cos ((a-b-1) x)+\cos (x) \cos ((a-b-1) x)-b^3 \cos (x) \cos ((a-b+1) x)-b^2 \cos (x) \cos ((a-b+1) x)+b \cos (x) \cos ((a-b+1) x)+\cos (x) \cos ((a-b+1) x)+b^3 \cos (x) \cos ((a+b-1) x)+b^2 \cos (x) \cos ((a+b-1) x)-b \cos (x) \cos ((a+b-1) x)-\cos (x) \cos ((a+b-1) x)-b^3 \cos (x) \cos ((a+b+1) x)+b^2 \cos (x) \cos ((a+b+1) x)+b \cos (x) \cos ((a+b+1) x)-\cos (x) \cos ((a+b+1) x)-b^3 \sin (x) \sin ((a-b-1) x)+b^2 \sin (x) \sin ((a-b-1) x)+b \sin (x) \sin ((a-b-1) x)-\sin (x) \sin ((a-b-1) x)-b^3 \sin (x) \sin ((a-b+1) x)-b^2 \sin (x) \sin ((a-b+1) x)+b \sin (x) \sin ((a-b+1) x)+\sin (x) \sin ((a-b+1) x)-b^3 \sin (x) \sin ((a+b-1) x)-b^2 \sin (x) \sin ((a+b-1) x)+b \sin (x) \sin ((a+b-1) x)+\sin (x) \sin ((a+b-1) x)-b^3 \sin (x) \sin ((a+b+1) x)+b^2 \sin (x) \sin ((a+b+1) x)+b \sin (x) \sin ((a+b+1) x)-\sin (x) \sin ((a+b+1) x)}{4 (a-b-1) (a-b+1) (a+b-1) (a+b+1)}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 82 \[ \left \{ y \left ( x \right ) =\sin \left ( x \right ) {\it \_C2}+\cos \left ( x \right ) {\it \_C1}+{\frac {- \left ( a+b+1 \right ) \left ( a+ b-1 \right ) \cos \left ( x \left ( a-b \right ) \right ) +\cos \left ( \left ( a+b \right ) x \right ) \left ( a-b+1 \right ) \left ( a-b-1 \right ) }{2\,{a}^{4}+ \left ( -4\,{b}^{2}-4 \right ) {a}^{2}+2\,{b}^{4} -4\,{b}^{2}+2}} \right \} \]