7.5.18 problem 18

Internal problem ID [122]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 18
Date solved : Friday, February 07, 2025 at 07:53:00 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} \left (x +y\right ) y^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

dsolve((x+y(x))*diff(y(x),x)=1,y(x), singsol=all)
 

\[ y = -\operatorname {LambertW}\left (-c_1 \,{\mathrm e}^{-x -1}\right )-x -1 \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

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

\[ y(x)\to -W\left (c_1 \left (-e^{-x-1}\right )\right )-x-1 \]