Internal problem ID [9907]
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: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y y^{\prime }-y-A=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 30
dsolve(y(x)*diff(y(x),x)-y(x)=A,y(x), singsol=all)
\[ y \relax (x ) = -A \left (\LambertW \left (-\frac {{\mathrm e}^{-1-\frac {c_{1}}{A}-\frac {x}{A}}}{A}\right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 28
DSolve[y[x]*y'[x]-y[x]==A,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -A \left (1+\text {ProductLog}\left (-\frac {e^{-\frac {A+x+c_1}{A}}}{A}\right )\right ) \\ \end{align*}