22.38 problem 38

Internal problem ID [10687]

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. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable equations and their solutions
Problem number: 38.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]

\[ \boxed {y y^{\prime }-y=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49}} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-12/48*x+6/49*A*(x^(1/2)+8*A+5*A^2*x^(-1/2)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y[x]*y'[x]-y[x]==-12/48*x+6/49*A*(x^(1/2)+8*A+5*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved