4.444   ODE No. 1444

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

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

Mathematica: cpu = 1.510692 (sec), leaf count = 36 $$\text{DSolve}[y^{″}(x)=-by(x)f(x{)}^{2a}-\frac{a{f}^{\prime }(x)y^{\prime }(x)}{f(x)},y(x),x]$$

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