Internal problem ID [13072]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {\left (y-x \right ) y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.022 (sec). Leaf size: 20
DSolve[(y[x]-x)*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to W\left (c_1 \left (-e^{-x-1}\right )\right )+x+1 \]