4.79   ODE No. 1079

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

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

Mathematica: cpu = 0.237530 (sec), leaf count = 135 $$\{\{y(x)\to \frac{1}{2}(e^{c_2+{\int }_1^x-i\sqrt{b}f(K[1]{)}^{a}dK[1]}-2c_1\exp (-c_2-{\int }_1^x-i\sqrt{b}f(K[1]{)}^{a}dK[1]))\},\{y(x)\to \frac{1}{2}(e^{c_2+{\int }_1^{x}i\sqrt{b}f(K[2]{)}^{a}dK[2]}-2c_1{e}^{-c_2-{\int }_1^{x}i\sqrt{b}f(K[2]{)}^{a}dK[2]})\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 37 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\int i{\left(f\left(x\right)\right)}^a\sqrt{b}\mathrm{d}x}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\int i{\left(f\left(x\right)\right)}^a\sqrt{b}\mathrm{d}x}\}$$