2.329   ODE No. 329

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

$$x^{n}y(x{)}^m(ax{y}^{\prime }(x)+by(x))+\alpha x{y}^{\prime }(x)+\beta y(x)=0$$ ✓ Mathematica : cpu = 0.430246 (sec), leaf count = 97

$$\text{Solve}[\frac{m((a\beta -\alpha b)\log (x^{n}y(x{)}^m(bm-an)-\alpha n+\beta m)+\alpha (bm-an)\log (y(x)(\beta m-\alpha n))+\beta \log (x)(bm-an))}{(bm-an)(\beta m-\alpha n)}=c_1,y(x)]$$

✓ Maple : cpu = 0.385 (sec), leaf count = 71

$$\{{\left({\left(y\left(x\right)\right)}^m\right)}^{\alpha (an-bm)}{x}^{\beta m(an-bm)}{(x^n(an-bm){\left(y\left(x\right)\right)}^m-\beta m+\alpha n)}^{-a\beta m+\alpha bm}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$