4.18   ODE No. 1018

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

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

Mathematica: cpu = 0.021503 (sec), leaf count = 55 $$\left\{\{y(x)\to c_1{J}_0\left(\frac{2\sqrt{a}\sqrt{e^{bx}}}{b}\right)+2c_2{Y}_0\left(\frac{2\sqrt{a}\sqrt{e^{bx}}}{b}\right)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 39 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_0\left(2\frac{\sqrt{a}{\mathrm{e}}^{1/2bx}}{b}\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_0\left(2\frac{\sqrt{a}{\mathrm{e}}^{1/2bx}}{b}\right)\}$$