\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {y \left ( x \right ) }{{x}^{4}} \left ( {{\rm e}^{2\,{x}^{-1}}}-{v}^{2} \right ) }=0} \]
Mathematica: cpu = 0.559571 (sec), leaf count = 173 \[ \left \{\left \{y(x)\to \frac {c_1 2^{v+\frac {v+1}{2}} \left (e^{2/x}\right )^{\frac {v+1}{2}-\frac {1}{2}} \left (-e^{2/x}\right )^{\frac {1}{2} (-v-1)+\frac {1}{2}} I_v\left (\sqrt {-e^{2/x}}\right )}{\log \left (e^{2/x}\right )}+\frac {c_2 (-1)^{-v} 2^{v+\frac {v+1}{2}} \left (e^{2/x}\right )^{\frac {v+1}{2}-\frac {1}{2}} \left (-e^{2/x}\right )^{\frac {1}{2} (-v-1)+\frac {1}{2}} K_v\left (\sqrt {-e^{2/x}}\right )}{\log \left (e^{2/x}\right )}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 23 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x{{\sl J}_{v}\left ({{\rm e}^{ {x}^{-1}}}\right )}+{\it \_C2}\,x{{\sl Y}_{v}\left ({{\rm e}^{{x}^{-1}}} \right )} \right \} \]