3.329   ODE No. 329

$$\boxed{{\displaystyle {\left(y\left(x\right)\right)}^m{x}^n(ax\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+by\left(x\right))+\alpha x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+\beta y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.313540 (sec), leaf count = 102 $$\text{Solve}[\frac{m((a\beta -\alpha b)\log (x^{n}y(x{)}^m(bm-an)-\alpha n+\beta m)+\beta \log (x)(bm-an))}{(bm-an)(\beta m-\alpha n)}+\frac{\alpha m\log (\beta my(x)-\alpha ny(x))}{\beta m-\alpha n}=c_1,y(x)]$$

Maple: cpu = 0.249 (sec), leaf count = 78 $$\{x^{a\beta mn-b\beta m^2}{\left({\left(y\left(x\right)\right)}^m\right)}^{a\alpha n-\alpha bm}{({\left(y\left(x\right)\right)}^m{x}^{n}na-{\left(y\left(x\right)\right)}^{m}m{x}^{n}b+\alpha n-\beta m)}^{-a\beta m+\alpha bm}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$