\[ a e^{-2 x} y(x)+y''(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.0175565 (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 = 0.01 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {{\rm e}^{-x}}\sqrt {a} \right ) +{\it \_C2}\,\cos \left ( {{\rm e}^{-x}}\sqrt {a} \right ) \right \} \]