\[ \boxed { {a}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a \left ( {a}^{2}-2\,b{{\rm e}^{-ax}} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{b}^{2}{{\rm e}^{-2\,ax}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.032 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {{a}^{3}x+2 \,b{{\rm e}^{-ax}}}{2\,{a}^{2}}}}}\sinh \left ( {\frac {ax}{2}} \right ) +{\it \_C2}\,{{\rm e}^{-{\frac {{a}^{3}x+2\,b{{\rm e}^{-ax}} }{2\,{a}^{2}}}}}\cosh \left ( {\frac {ax}{2}} \right ) \right \} \]