3.552   ODE No. 552

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

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

Mathematica: cpu = 0.164021 (sec), leaf count = 39 $$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}g(K[1]{)}^{-1/n}dK[1]\mathrm{\&}][{\int }_1^{x}f(K[2]{)}^{\frac{1}{n}}dK[2]+c_1]\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 43 $$\{{\int }^{y\left(x\right)}{\left(g\left(\mathit{\_}\mathit{a}\right)\right)}^{-n^{-1}}d\mathit{\_}\mathit{a}+{\int }^x-\frac{\sqrt[n]{f\left(\mathit{\_}\mathit{a}\right)g\left(y\left(x\right)\right)}}{\sqrt[n]{g\left(y\left(x\right)\right)}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$