\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{{\rm e}^{bx}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.021503 (sec), leaf count = 55 \[ \left \{\left \{y(x)\to c_1 J_0\left (\frac {2 \sqrt {a} \sqrt {e^{b x}}}{b}\right )+2 c_2 Y_0\left (\frac {2 \sqrt {a} \sqrt {e^{b x}}}{b}\right )\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{0}\left (2\,{\frac { \sqrt {a}{{\rm e}^{1/2\,bx}}}{b}}\right )}+{\it \_C2}\,{{\sl Y}_{0 }\left (2\,{\frac {\sqrt {a}{{\rm e}^{1/2\,bx}}}{b}}\right )} \right \} \]