\[ y''(x)=-\frac {\left (e^{2/x}-v^2\right ) y(x)}{x^4} \] ✓ Mathematica : cpu = 0.588664 (sec), leaf count = 100
\[\left \{\left \{y(x)\to \frac {(-1)^{-v} 2^{\frac {3 v}{2}+\frac {1}{2}} \left (-e^{2/x}\right )^{-v/2} \left (e^{2/x}\right )^{v/2} \left (c_1 (-1)^v I_v\left (\sqrt {-e^{2/x}}\right )+c_2 K_v\left (\sqrt {-e^{2/x}}\right )\right )}{\log \left (e^{2/x}\right )}\right \}\right \}\]
✓ Maple : cpu = 0.048 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) =x \left ( {{\sl Y}_{v}\left ({{\rm e}^{{x}^{-1}}}\right )}{\it \_C2}+{{\sl J}_{v}\left ({{\rm e}^{{x}^{-1}}}\right )}{\it \_C1} \right ) \right \} \]