22.70 problem 70

Internal problem ID [10719]

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: 70.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {y y^{\prime }-y=-\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{\frac {1}{7}}}+\frac {280 A}{x^{\frac {5}{7}}}-\frac {400 A^{2}}{x^{\frac {9}{7}}}\right )}{9}} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)-y(x)=-21/100*x+7/9*A^2*(123*x^(-1/7)+280*A*x^(-5/7)-400*A^2*x^(-9/7)),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]==-21/100*x+7/9*A^2*(123*x^(-1/7)+280*A*x^(-5/7)-400*A^2*x^(-9/7)),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved