Internal problem ID [8586]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 250.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (B x y+A \,x^{2}+x a +b y+c \right ) y^{\prime }+A x y+\beta y=B g \left (x \right )^{2}-x \alpha -\gamma } \]
✗ Solution by Maple
dsolve((B*x*y(x)+A*x^2+a*x+b*y(x)+c)*diff(y(x),x)-B*g(x)^2+A*x*y(x)+alpha*x+beta*y(x)+gamma=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(B*x*y[x]+A*x^2+a*x+b*y[x]+c)*y'[x]-B*g[x]^2+A*x*y[x]+\[Alpha]*x+\[Beta]*y[x]+\[Gamma]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out