\[ -a^2 y'(x)+2 a^2 y(x)-2 y''(x)+y^{(3)}(x)-\sinh (x)=0 \] ✓ Mathematica : cpu = 0.0826201 (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 = 0.086 (sec), leaf count = 113
\[ \left \{ y \left ( x \right ) ={\frac {1}{6\,{a}^{4}-30\,{a}^{2}+24} \left ( \left ( 6\,{\it \_C3}\,{a}^{4}-30\,{\it \_C3}\,{a}^{2}+24\,{\it \_C3} \right ) {{\rm e}^{-ax}}+6\, \left ( a-1 \right ) \left ( {\it \_C1}\,{a}^{2}+1/6\,\sinh \left ( 3\,x \right ) -4\,{\it \_C1}-1/6\,\cosh \left ( 3\,x \right ) \right ) \left ( a+1 \right ) {{\rm e}^{2\,x}}+ \left ( 6\,{\it \_C2}\,{a}^{4}-30\,{\it \_C2}\,{a}^{2}+24\,{\it \_C2} \right ) {{\rm e}^{ax}}+3\,{{\rm e}^{x}}{a}^{2}-12\,{{\rm e}^{x}}+3\,{{\rm e}^{-x}} \right ) } \right \} \]