67.5.17 problem 6.7 (e)

Internal problem ID [16415]
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 : Thursday, October 02, 2025 at 01:29:52 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

ode:=(y(x)-x)*diff(y(x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 20

ode=(y[x]-x)*D[y[x],x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to W\left (c_1 \left (-e^{-x-1}\right )\right )+x+1 \end{align*}

✓ Sympy. Time used: 0.408 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x + y(x))*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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