\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a{{\rm e}^{-2\,x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.016502 (sec), leaf count = 37 \[ \left \{\left \{y(x)\to c_1 \cos \left (\sqrt {a} e^{-x}\right )-c_2 \sin \left (\sqrt {a} e^{-x}\right )\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {{\rm e}^{-x}} \sqrt {a} \right ) +{\it \_C2}\,\cos \left ( {{\rm e}^{-x}}\sqrt {a} \right ) \right \} \]