\[ y''(x)=-\frac {\left (e^{2/x}-v^2\right ) y(x)}{x^4} \] ✓ Mathematica : cpu = 0.479527 (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 = 0.398 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) =x \left ( {{\sl J}_{v}\left ({{\rm e}^{{x}^{-1}}}\right )}{\it \_C1}+{{\sl Y}_{v}\left ({{\rm e}^{{x}^{-1}}}\right )}{\it \_C2} \right ) \right \} \]