61.25.3 problem 3

Internal problem ID [12496]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.4-2.
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 03:18:01 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+a k \,x^{2}+b x +c \right ) y^{\prime }&=-a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s \end{align*}

✗ Solution by Maple

dsolve((y(x)+a*k*x^2+b*x+c)*diff(y(x),x)=-a*y(x)^2+2*a*k*x*y(x)+m*y(x)+k*(k+b-m)*x+s,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(y[x]+a*k*x^2+b*x+c)*D[y[x],x]==-a*y[x]^2+2*a*k*x*y[x]+m*y[x]+k*(k+b-m)*x+s,y[x],x,IncludeSingularSolutions -> True]
 

Timed out