Internal problem ID [3127]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _dAlembert]
\[ \boxed {y^{\prime } \ln \left (-y+x \right )-\ln \left (-y+x \right )=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)*ln(x-y(x))=1+ln(x-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{\operatorname {LambertW}\left (\left (c_{1} -x \right ) {\mathrm e}^{-1}\right )+1}+x \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 26
DSolve[y'[x]*Log[x-y[x]]==1+Log[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[(x-y(x)) (-\log (x-y(x)))-y(x)=c_1,y(x)] \]