Internal problem ID [10724]
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: 75.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-y=2 a^{2} \lambda \sin \left (2 \lambda x \right )+2 a \sin \left (\lambda x \right )} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-y(x)=2*a^2*lambda*sin(2*lambda*x)+2*a*sin(lambda*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]-y[x]==2*a^2*\[Lambda]*Sin[2*\[Lambda]*x]+2*a*Sin[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
Not solved