\[ -a^2 y'(x)+2 a^2 y(x)+y^{(3)}(x)-2 y''(x)-\sinh (x)=0 \] ✓ Mathematica : cpu = 0.0822642 (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 = 0.09 (sec), leaf count = 467
\[ \left \{ y \left ( x \right ) =-{\frac {9\,{{\rm e}^{-ax}}\sinh \left ( \left ( a+1 \right ) x \right ) a+9\,{{\rm e}^{-ax}}\cosh \left ( \left ( a+1 \right ) x \right ) a-3\,{{\rm e}^{-ax}}\cosh \left ( \left ( a-1 \right ) x \right ) a-3\,{{\rm e}^{-ax}}\sinh \left ( \left ( a-1 \right ) x \right ) a+3\,{{\rm e}^{ax}}\sinh \left ( \left ( a+1 \right ) x \right ) a-3\,{{\rm e}^{ax}}\cosh \left ( \left ( a+1 \right ) x \right ) a+9\,{{\rm e}^{ax}}\cosh \left ( \left ( a-1 \right ) x \right ) a-9\,{{\rm e}^{ax}}\sinh \left ( \left ( a-1 \right ) x \right ) a+2\,{{\rm e}^{2\,x}}\sinh \left ( 3\,x \right ) a-3\,{{\rm e}^{ax}}\cosh \left ( \left ( a+1 \right ) x \right ) {a}^{2}+3\,{{\rm e}^{ax}}\cosh \left ( \left ( a-1 \right ) x \right ) {a}^{2}-3\,{{\rm e}^{ax}}\sinh \left ( \left ( a-1 \right ) x \right ) {a}^{2}-3\,{{\rm e}^{-ax}}\sinh \left ( \left ( a+1 \right ) x \right ) {a}^{2}-3\,{{\rm e}^{-ax}}\cosh \left ( \left ( a+1 \right ) x \right ) {a}^{2}+3\,{{\rm e}^{-ax}}\cosh \left ( \left ( a-1 \right ) x \right ) {a}^{2}+3\,{{\rm e}^{-ax}}\sinh \left ( \left ( a-1 \right ) x \right ) {a}^{2}-6\,\sinh \left ( x \right ) {{\rm e}^{2\,x}}a+6\,{{\rm e}^{2\,x}}\cosh \left ( x \right ) a-2\,{{\rm e}^{2\,x}}\cosh \left ( 3\,x \right ) a+3\,{{\rm e}^{ax}}\sinh \left ( \left ( a+1 \right ) x \right ) {a}^{2}-6\,{{\rm e}^{2\,x}}\cosh \left ( x \right ) {a}^{3}+2\,{{\rm e}^{2\,x}}\cosh \left ( 3\,x \right ) {a}^{3}-2\,{{\rm e}^{2\,x}}\sinh \left ( 3\,x \right ) {a}^{3}+6\,\sinh \left ( x \right ) {{\rm e}^{2\,x}}{a}^{3}-6\,{{\rm e}^{ax}}\sinh \left ( \left ( a+1 \right ) x \right ) +6\,{{\rm e}^{ax}}\cosh \left ( \left ( a+1 \right ) x \right ) +6\,{{\rm e}^{ax}}\cosh \left ( \left ( a-1 \right ) x \right ) -6\,{{\rm e}^{ax}}\sinh \left ( \left ( a-1 \right ) x \right ) -6\,{{\rm e}^{-ax}}\sinh \left ( \left ( a+1 \right ) x \right ) -6\,{{\rm e}^{-ax}}\cosh \left ( \left ( a+1 \right ) x \right ) -6\,{{\rm e}^{-ax}}\cosh \left ( \left ( a-1 \right ) x \right ) -6\,{{\rm e}^{-ax}}\sinh \left ( \left ( a-1 \right ) x \right ) }{12\,a \left ( {a}^{2}-4 \right ) \left ( a+1 \right ) \left ( a-1 \right ) }}+{\it \_C1}\,{{\rm e}^{2\,x}}+{\it \_C2}\,{{\rm e}^{ax}}+{\it \_C3}\,{{\rm e}^{-ax}} \right \} \]