2.52   ODE No. 52

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

$$-ay(x{)}^n-b{x}^{\frac{n}{1-n}}+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 143.361 (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 = 0.211 (sec), leaf count = 61

$$\{-{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}1x^{\frac{n}{n-1}}{((ax(n-1){\mathit{\_}\mathit{a}}^n+\mathit{\_}\mathit{a})x^{\frac{n}{n-1}}+b(n-1)x)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}(n-1)+\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$