73.5.17 problem 6.7 (e)

Internal problem ID [15128]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (e)
Date solved : Tuesday, January 28, 2025 at 07:34:57 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve((y(x)-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: 20

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

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