61.22.59 problem 59

Internal problem ID [12384]
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 : 59
Date solved : Tuesday, January 28, 2025 at 02:55:25 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \end{align*}

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-4/25*x+1/50*A*(7*x^(1/2)+49*A+6*A^2*x^(-1/2)),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]==-4/25*x+1/50*A*(7*x^(1/2)+49*A+6*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
 

Not solved