\[ -a^2 y'(x)+2 a^2 y(x)+y^{(3)}(x)-2 y''(x)-\sinh (x)=0 \] ✓ Mathematica : cpu = 0.0863302 (sec), leaf count = 95
\[\left \{\left \{y(x)\to \frac {e^{-x} \left (3 a^2 e^{2 x}-a^2-3 e^{2 x}-12 e^x \sinh (x)-6 e^x \cosh (x)+1\right )}{6 (a-2) (a+2) \left (a^2-1\right )}+c_1 e^{-a x}+c_3 e^{a x}+c_2 e^{2 x}\right \}\right \}\] ✓ Maple : cpu = 0.121 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={\frac {1}{6\,{a}^{4}-30\,{a}^{2}+24} \left ( -9\,{{\rm e}^{ax}} \left ( {{\rm e}^{x}}-1/3\,{{\rm e}^{-x}} \right ) {{\rm e}^{-ax}}+3\, \left ( a+1 \right ) \left ( a-1 \right ) \left ( {{\rm e}^{-x}}-1/3\,\cosh \left ( 3\,x \right ) +1/3\,\sinh \left ( 3\,x \right ) \right ) {{\rm e}^{2\,x}} \right ) }+{\it \_C1}\,{{\rm e}^{2\,x}}+{{\rm e}^{ax}}{\it \_C2}+{\it \_C3}\,{{\rm e}^{-ax}} \right \} \]