61.24.12 problem 12

Internal problem ID [12425]
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 : 12
Date solved : Tuesday, January 28, 2025 at 03:01:16 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=((m+2*L-3)*x+n-2*L+3)*1/x*y(x)+((m-L-1)*x^2+(n-m-2*L+3)*x-n+L-2)*x^(1-2*L),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]==((m+2*L-3)*x+n-2*L+3)*1/x*y[x]+((m-L-1)*x^2+(n-m-2*L+3)*x-n+L-2)*x^(1-2*L),y[x],x,IncludeSingularSolutions -> True]
 

Timed out