23.12 problem 12

Internal problem ID [10737]

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 1.3.2. Equations of the form \(y y'=f(x) y+1\)
Problem number: 12.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {y y^{\prime }-\sin \left (\lambda x \right ) y a=1} \]

✗ Solution by Maple

dsolve(y(x)*diff(y(x),x)=a*sin(lambda*x)*y(x)+1,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*Sin[\[Lambda]*x]*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved