24.79 problem 79

Internal problem ID [10816]

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 1.3.3-2. Equations of the form \(y y'=f_1(x) y+f_0(x)\)
Problem number: 79.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {y y^{\prime }-a x \cos \left (\lambda \,x^{2}\right ) y=x} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=a*x*cos(lambda*x^2)*y(x)+x,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y[x]*y'[x]==a*x*Cos[\[Lambda]*x^2]*y[x]+x,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved