2.291   ODE No. 291

\[ y'(x) \left (b (\alpha x+\beta y(x))^2-\beta (a x+b y(x))\right )-\alpha (a x+b y(x))+a (\alpha x+\beta y(x))^2=0 \] Mathematica : cpu = 1.1306 (sec), leaf count = 39


\[\text {Solve}\left [\frac {a \beta \left (\log (a x+b y(x))+\frac {1}{\alpha x+\beta y(x)}\right )}{a \beta -\alpha b}=c_1,y(x)\right ]\] Maple : cpu = 0.16 (sec), leaf count = 50


\[y \relax (x ) = \frac {-a x +{\mathrm e}^{\RootOf \left (c_{1} a \beta x -c_{1} \alpha b x -\textit {\_Z} a \beta x +\textit {\_Z} \alpha b x -c_{1} \beta \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} \beta +b \right )}}{b}\]