4.78   ODE No. 1078

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+f\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(1/4{\left(f\left(x\right)\right)}^2+1/2\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)+a)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.073009 (sec), leaf count = 73 $$\left\{\{y(x)\to c_1\exp (-\frac{1}{2}{\int }_1^{x}f(K[1])dK[1]-\sqrt{-a}x)+\frac{c_2{e}^{\sqrt{-a}x-\frac{1}{2}{\int }_1^{x}f(K[1])dK[1]}}{2\sqrt{-a}}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 39 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{\int f\left(x\right)\mathrm{d}x}{2}}\sinh \left(\sqrt{-a}x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{\int f\left(x\right)\mathrm{d}x}{2}}\cosh \left(\sqrt{-a}x\right)\}$$