Internal problem ID [10733]
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: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y=1} \]
✗ Solution by Maple
dsolve(y(x)*diff(y(x),x)=(a*exp(lambda*x)+b*exp(-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*Exp[\[Lambda]*x]+b*Exp[-\[Lambda]*x])*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
Not solved