4.17   ODE No. 1017

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

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

Mathematica: cpu = 0.027504 (sec), leaf count = 46 $$\left\{\{y(x)\to c_1\mathrm{\Gamma }(1-v)J_{-v}\left(\sqrt{e^{2x}}\right)+c_2\mathrm{\Gamma }(v+1)J_v\left(\sqrt{e^{2x}}\right)\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 17 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_v\left({\mathrm{e}}^x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_v\left({\mathrm{e}}^x\right)\}$$