3.128   ODE No. 128

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

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

Mathematica: cpu = 5.142653 (sec), leaf count = 39 $$\text{Solve}[{\int }_1^{x^{a}y(x)}\frac{1}{g(K[1])}dK[1]={\int }_1^{x}K[2{]}^{a-1}f(K[2])dK[2]+c_1,y(x)]$$

Maple: cpu = 0.203 (sec), leaf count = 33 $$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\int x^{a-1}f\left(x\right)\mathrm{d}x+{\int }^{\mathit{\_}\mathit{Z}}{\left(g\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}{x^a}\}$$