28.1.13 problem 13

Internal problem ID [4319]
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
Date solved : Monday, January 27, 2025 at 09:02:15 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} \left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 26

dsolve((1-exp(- y(x)/x))*diff(y(x),x)+(1- y(x)/x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-c_{1} \operatorname {LambertW}\left (-{\mathrm e}^{-\frac {1}{c_{1} x}}\right ) x -1}{c_{1}} \]

✓ Solution by Mathematica

Time used: 60.202 (sec). Leaf size: 29

DSolve[(1-Exp[-y[x]/x])*D[y[x],x]+(1-y[x]/x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x W\left (-e^{-\frac {e^{c_1}}{x}}\right )-e^{c_1} \]