61.22.15 problem 15

Internal problem ID [12340]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 02:48:13 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-3/16*x+5*A*x^(-1/3)-12*A^2*x^(-5/3),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]-y[x]==-3/16*x+5*A*x^(-1/3)-12*A^2*x^(-5/3),y[x],x,IncludeSingularSolutions -> True]
 

Not solved