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]
\[ \boxed {\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve((1-exp(- y(x)/x))*diff(y(x),x)+(1- y(x)/x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-{\mathrm e}^{-\frac {1}{c_{1} x}}\right ) c_{1} x +1}{c_{1}} \]
✓ Solution by Mathematica
Time used: 60.185 (sec). Leaf size: 29
DSolve[(1-Exp[-y[x]/x])*y'[x]+(1-y[x]/x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x W\left (-e^{-\frac {e^{c_1}}{x}}\right )-e^{c_1} \\ \end{align*}