\[ a e^{b x} y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0157518 (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 = 0.063 (sec), leaf count = 39
\[y \relax (x ) = c_{1} \BesselJ \left (0, \frac {2 \sqrt {a}\, {\mathrm e}^{\frac {b x}{2}}}{b}\right )+c_{2} \BesselY \left (0, \frac {2 \sqrt {a}\, {\mathrm e}^{\frac {b x}{2}}}{b}\right )\]