61.22.68 problem 68

Internal problem ID [12393]
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 : 68
Date solved : Tuesday, January 28, 2025 at 02:56:36 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=-\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{{1}/{5}}}-\frac {7 A^{3}}{20 x^{{4}/{5}}} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-10/49*x+13/5*A^2*x^(-1/5)-7/20*A^3*x^(-4/5),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]==-10/49*x+13/5*A^2*x^(-1/5)-7/20*A^3*x^(-4/5),y[x],x,IncludeSingularSolutions -> True]
 

Not solved