2.291   ODE No. 291

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

$$y^{\prime }(x)(b(\alpha x+\beta y(x){)}^2-\beta (ax+by(x)))-\alpha (ax+by(x))+a(\alpha x+\beta y(x){)}^2=0$$ ✓ Mathematica : cpu = 1.04395 (sec), leaf count = 39

$$\text{Solve}[\frac{a\beta (\log (ax+by(x))+\frac{1}{\alpha x+\beta y(x)})}{a\beta -\alpha b}=c_1,y(x)]$$

✓ Maple : cpu = 0.189 (sec), leaf count = 50

$$\{y\left(x\right)=\frac{-ax+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\mathit{\_}\mathit{C}\mathit{1}a\beta x-\mathit{\_}\mathit{C}\mathit{1}\alpha bx-\mathit{\_}\mathit{Z}a\beta x+\mathit{\_}\mathit{Z}\alpha bx-\mathit{\_}\mathit{C}\mathit{1}\beta {\mathrm{e}}^{\mathit{\_}\mathit{Z}}+{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}\beta +b)}}{b}\}$$