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 = 0.832767 (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 = 0.466 (sec), leaf count = 73

$$\{x^{-a\beta mn+b\beta m^2}{\left(y{\left(x\right)}^m\right)}^{-an\alpha +bm\alpha }{(\alpha n-\beta m+(an-bm)x^{n}y{\left(x\right)}^m)}^{(a\beta -\alpha b)m}-c_1=0\}$$