61.24.60 problem 60

Internal problem ID [12473]
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 1.3.3-2.
Problem number : 60
Date solved : Tuesday, January 28, 2025 at 03:14:22 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y&=n \,x^{2 n} \left (x -a \right )^{-2 n -3} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-((n+1)*x-a*n)*x^(n-1)*(x-a)^(-n-2)*y(x)=n*x^(2*n)*(x-a)^(-2*n-3),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[y[x],x]-((n+1)*x-a*n)*x^(n-1)*(x-a)^(-n-2)*y[x]==n*x^(2*n)*(x-a)^(-2*n-3),y[x],x,IncludeSingularSolutions -> True]
 

Not solved