22.50 problem 50

Internal problem ID [10699]

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: 50.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {y y^{\prime }-y=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right )} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=2*x+2*A*(-10*x^(1/2)+19*A+30*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]==2*x+2*A*(-10*x^(1/2)+19*A+30*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved