61.25.6 problem 6

Internal problem ID [12499]
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 : 6
Date solved : Tuesday, January 28, 2025 at 03:18:47 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y y^{\prime }&=a y^{2}+b y+c \,x^{n}+s \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved