\[ a e^{b x} y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0160755 (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 = 0.52 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{0}\left (2\,{\frac {\sqrt {a}{{\rm e}^{1/2\,bx}}}{b}}\right )}+{\it \_C2}\,{{\sl Y}_{0}\left (2\,{\frac {\sqrt {a}{{\rm e}^{1/2\,bx}}}{b}}\right )} \right \} \]