Internal problem ID [7871]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 291.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {\left (b \left (\beta y+x \alpha \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+x \alpha \right )^{2}-\alpha \left (a x +b y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 50
dsolve((b*(beta*y(x)+alpha*x)^2-beta*(b*y(x)+a*x))*diff(y(x),x)+a*(beta*y(x)+alpha*x)^2-alpha*(b*y(x)+a*x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-a x +{\mathrm e}^{\RootOf \left (c_{1} a \beta x -c_{1} \alpha b x -\textit {\_Z} a \beta x +\textit {\_Z} \alpha b x -c_{1} \beta \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} \beta +b \right )}}{b} \]
✓ Solution by Mathematica
Time used: 1.314 (sec). Leaf size: 39
DSolve[(b*(\[Beta]*y[x]+alpha*x)^2-\[Beta]*(b*y[x]+a*x))*y'[x]+a*(\[Beta]*y[x]+alpha*x)^2-alpha*(b*y[x]+a*x)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {a \beta \left (\log (a x+b y(x))+\frac {1}{\alpha x+\beta y(x)}\right )}{a \beta -\alpha b}=c_1,y(x)\right ] \]