\[ \left (e^{2 x}-v^2\right ) y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0150592 (sec), leaf count = 46
DSolve[(E^(2*x) - v^2)*y[x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {Gamma}(1-v) \operatorname {BesselJ}\left (-v,\sqrt {e^{2 x}}\right )+c_2 \operatorname {Gamma}(v+1) \operatorname {BesselJ}\left (v,\sqrt {e^{2 x}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.032 (sec), leaf count = 17
dsolve(diff(diff(y(x),x),x)+(exp(2*x)-v^2)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (v , {\mathrm e}^{x}\right )+c_{2} \operatorname {BesselY}\left (v , {\mathrm e}^{x}\right )\]