Internal problem ID [9979]
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: 73.
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}+a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}-b=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)-y(x)=a^2*lambda*exp(2*lambda*x)-a*(b*lambda+1)*exp(lambda*x)+b,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*(b*\[Lambda]+1)*Exp[\[Lambda]*x]+b,y[x],x,IncludeSingularSolutions -> True]
Not solved