2.552   ODE No. 552

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

$$y^{\prime }(x{)}^n-f(x)g(y(x))=0$$ ✓ Mathematica : cpu = 0.0326237 (sec), leaf count = 41

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}g(K[1]{)}^{-1/n}dK[1]\mathrm{\&}][{\int }_1^{x}f(K[2]{)}^{\frac{1}{n}}dK[2]+c_1]\}\right\}$$ ✓ Maple : cpu = 0.384 (sec), leaf count = 43

$$\{{\int }^{y\left(x\right)}{\left(g\left(\mathit{\_}\mathit{a}\right)\right)}^{-n^{-1}}d\mathit{\_}\mathit{a}+{\int }^x-\frac{\sqrt[n]{f\left(\mathit{\_}\mathit{a}\right)g\left(y\left(x\right)\right)}}{\sqrt[n]{g\left(y\left(x\right)\right)}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$