\[ -a^2 y'(x)+2 a^2 y(x)+y^{(3)}(x)-2 y''(x)-\sinh (x)=0 \] ✓ Mathematica : cpu = 0.105105 (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 = 0.08 (sec), leaf count = 214
\[ \left \{ y \left ( x \right ) ={\frac {1}{12\,{a}^{5}-60\,{a}^{3}+48\,a} \left ( -3\, \left ( a+1 \right ) \left ( \left ( a-2 \right ) {{\rm e}^{-ax}}+{{\rm e}^{ax}} \left ( a+2 \right ) \right ) \cosh \left ( \left ( a-1 \right ) x \right ) +3\, \left ( a-1 \right ) \left ( \left ( a-2 \right ) {{\rm e}^{-ax}}+{{\rm e}^{ax}} \left ( a+2 \right ) \right ) \cosh \left ( \left ( a+1 \right ) x \right ) +3\, \left ( \left ( -a+2 \right ) {{\rm e}^{-ax}}+{{\rm e}^{ax}} \left ( a+2 \right ) \right ) \left ( a+1 \right ) \sinh \left ( \left ( a-1 \right ) x \right ) +12\, \left ( \left ( \left ( a/4-1/2 \right ) {{\rm e}^{-ax}}-1/4\,{{\rm e}^{ax}} \left ( a+2 \right ) \right ) \sinh \left ( \left ( a+1 \right ) x \right ) + \left ( \left ( {\it \_C3}\,{a}^{2}-4\,{\it \_C3} \right ) {{\rm e}^{-ax}}+ \left ( {\it \_C2}\,{a}^{2}-4\,{\it \_C2} \right ) {{\rm e}^{ax}}+{{\rm e}^{2\,x}} \left ( {a}^{2}{\it \_C1}+1/6\,\sinh \left ( 3\,x \right ) -4\,{\it \_C1}+1/2\,\cosh \left ( x \right ) -1/2\,\sinh \left ( x \right ) -1/6\,\cosh \left ( 3\,x \right ) \right ) \right ) \left ( a+1 \right ) a \right ) \left ( a-1 \right ) \right ) } \right \} \]