\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {{\rm e}^{2\,x}}-{v}^{2} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.027504 (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 = 0.063 (sec), leaf count = 17 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{v}\left ({{\rm e}^{x }}\right )}+{\it \_C2}\,{{\sl Y}_{v}\left ({{\rm e}^{x}}\right )} \right \} \]