ODE No. 1344

$$y^{″}(x)=-\frac{(e^{2/x}-v^2)y(x)}{x^4}$$ ✓ Mathematica : cpu = 0.442009 (sec), leaf count = 173

DSolve[Derivative[2][y][x] == -(((E^(2/x) - v^2)*y[x])/x^4),y[x],x]
 

$$\left\{\{y(x)\to \frac{c_1{2}^{v+\frac{v+1}{2}}{\left(e^{2/x}\right)}^{\frac{v+1}{2}-\frac{1}{2}}{(-e^{2/x})}^{\frac{1}{2}(-v-1)+\frac{1}{2}}{I}_v\left(\sqrt{-e^{2/x}}\right)}{\log \left(e^{2/x}\right)}+\frac{c_2(-1{)}^{-v}{2}^{v+\frac{v+1}{2}}{\left(e^{2/x}\right)}^{\frac{v+1}{2}-\frac{1}{2}}{(-e^{2/x})}^{\frac{1}{2}(-v-1)+\frac{1}{2}}{K}_v\left(\sqrt{-e^{2/x}}\right)}{\log \left(e^{2/x}\right)}\}\right\}$$ ✓ Maple : cpu = 0.06 (sec), leaf count = 23

dsolve(diff(diff(y(x),x),x) = -(exp(2/x)-v^2)/x^4*y(x),y(x))
 

$$y\left(x\right)=x(\mathrm{BesselY}(v,{\mathrm{e}}^{\frac{1}{x}})c_2+\mathrm{BesselJ}(v,{\mathrm{e}}^{\frac{1}{x}})c_1)$$