61.25.5 problem 5

Internal problem ID [12498]
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 : 5
Date solved : Tuesday, January 28, 2025 at 03:18:44 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime }&=\left (a n \,x^{n}+c \,x^{n -1}\right ) y \end{align*}

✗ Solution by Maple

dsolve((y(x)+a*x^(n+1)+b*x^n)*diff(y(x),x)=(a*n*x^n+c*x^(n-1))*y(x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[(y[x]+a*x^(n+1)+b*x^n)*D[y[x],x]==(a*n*x^n+c*x^(n-1))*y[x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved