61.24.57 problem 57

Internal problem ID [12470]
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 : 57
Date solved : Tuesday, January 28, 2025 at 03:14:04 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-a*( (k-2)*x + 2*k - 3)*x^(-k)*y(x)=a^2*(k-2)*(x-1)^2*x^(1-2*k),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]-a*( (k-2)*x + 2*k - 3)*x^(-k)*y[x]==a^2*(k-2)*(x-1)^2*x^(1-2*k),y[x],x,IncludeSingularSolutions -> True]
 

Not solved