2.189   ODE No. 189

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

$$-ay(x{)}^n-b{x}^{(m+1)n}+x^{m(n-1)+n}{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.342692 (sec), leaf count = 91

$$\text{Solve}[{\int }_1^{{\left(\frac{a{x}^{-(m+1)n}}{b}\right)}^{\frac{1}{n}}y(x)}\frac{1}{K[1{]}^n-{\left(\frac{b^{1-n}(m+1{)}^n}{a}\right)}^{\frac{1}{n}}K[1]+1}dK[1]=b{x}^{m+1}\log (x){\left(\frac{a{x}^{-(m+1)n}}{b}\right)}^{\frac{1}{n}}+c_1,y(x)]$$ ✓ Maple : cpu = 0.266 (sec), leaf count = 60

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