Internal problem ID [2649]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 26
dsolve((1-exp(- y(x)/x))*diff(y(x),x)+(1- y(x)/x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\LambertW \left (-{\mathrm e}^{-\frac {1}{x c_{1}}}\right ) c_{1} x +1}{c_{1}} \]
✓ Solution by Mathematica
Time used: 1.966 (sec). Leaf size: 38
DSolve[(1-Exp[-y[x]/x])*y'[x]+(1-y[x]/x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \text {ProductLog}\left (-e^{-\frac {e^{c_1}}{x}}\right )-e^{c_1} \\ y(x)\to \text {ProductLog}(-1) (-x) \\ \end{align*}