78.8.18 problem 18

Internal problem ID [18216]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 11:39:49 AM
CAS classification : [[_homogeneous, `class C`], _exact, _dAlembert]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 26

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

\[ \text {Solve}[(x-y(x)) (-\log (x-y(x)))-y(x)=c_1,y(x)] \]