4.344   ODE No. 1344

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-\frac{y\left(x\right)}{x^4}({\mathrm{e}}^{2x^{-1}}-v^2)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.559571 (sec), leaf count = 173 $$\left\{\{y(x)\to \frac{c_1{2}^{v+\frac{v+1}{2}}{\left(e^{2/x}\right)}^{\frac{v+1}{2}-\frac{1}{2}}{(-e^{2/x})}^{\frac{1}{2}(-v-1)+\frac{1}{2}}{I}_v\left(\sqrt{-e^{2/x}}\right)}{\log \left(e^{2/x}\right)}+\frac{c_2(-1{)}^{-v}{2}^{v+\frac{v+1}{2}}{\left(e^{2/x}\right)}^{\frac{v+1}{2}-\frac{1}{2}}{(-e^{2/x})}^{\frac{1}{2}(-v-1)+\frac{1}{2}}{K}_v\left(\sqrt{-e^{2/x}}\right)}{\log \left(e^{2/x}\right)}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 23 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x{\mathit{J}}_v\left({\mathrm{e}}^{x^{-1}}\right)+\mathit{\_}\mathit{C}\mathit{2}x{\mathit{Y}}_v\left({\mathrm{e}}^{x^{-1}}\right)\}$$