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 = 1.27606 (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 = 0.161 (sec), leaf count = 50

$$\{y\left(x\right)=\frac{-ax+{\mathrm{e}}^{\mathrm{RootOf}(c_{1}a\beta x-c_1\alpha bx-\mathit{\text{\_Z}}a\beta x+\mathit{\text{\_Z}}\alpha bx-c_1\beta {\mathrm{e}}^{\mathit{\text{\_Z}}}+\mathit{\text{\_Z}}\beta {\mathrm{e}}^{\mathit{\text{\_Z}}}+b)}}{b}\}$$