\[ \left (e^{2 x}-v^2\right ) y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.019605 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 \Gamma (1-v) J_{-v}\left (\sqrt {e^{2 x}}\right )+c_2 \Gamma (v+1) J_v\left (\sqrt {e^{2 x}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.052 (sec), leaf count = 17
\[y \relax (x ) = c_{1} \BesselJ \left (v , {\mathrm e}^{x}\right )+c_{2} \BesselY \left (v , {\mathrm e}^{x}\right )\]