Internal problem ID [9980]
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: 74.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime } y-y-a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-{\mathrm e}^{\lambda x} a \lambda x -b \,{\mathrm e}^{\lambda x}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-y(x)=a^2*lambda*exp(2*lambda*x)+a*lambda*x*exp(lambda*x)+b*exp(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]==a^2*\[Lambda]*Exp[2*\[Lambda]*x]+a*\[Lambda]*x*Exp[\[Lambda]*x]+b*Exp[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
Not solved