3.52   ODE No. 52

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

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

Mathematica: cpu = 116.892343 (sec), leaf count = 115 $$\text{Solve}[{\int }_1^{y(x){\left(\frac{a{x}^{-\frac{n}{1-n}}}{b}\right)}^{\frac{1}{n}}}\frac{1}{-K[1]{\left(\frac{(-1{)}^n(n-1{)}^{-n}{b}^{1-n}}{a}\right)}^{\frac{1}{n}}+K[1{]}^n+1}dK[1]={\int }_1^{x}bK[2{]}^{\frac{n}{1-n}}{\left(\frac{aK[2{]}^{-\frac{n}{1-n}}}{b}\right)}^{\frac{1}{n}}dK[2]+c_1,y(x)]$$

Maple: cpu = 0.156 (sec), leaf count = 61 $$\{-{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}1x^{\frac{n}{n-1}}{((ax(n-1){\mathit{\_}\mathit{a}}^n+\mathit{\_}\mathit{a})x^{\frac{n}{n-1}}+b(n-1)x)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}(n-1)+\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$