67.7.27 problem 27

Internal problem ID [16472]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 27
Date solved : Thursday, October 02, 2025 at 01:34:47 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} 1-\left (x +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=1-(2*y(x)+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {x}{2}-1}}{2}\right )-\frac {x}{2}-1 \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 36

ode=1-(x+2*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=e^{y(x)} \int _1^{y(x)}2 e^{-K[1]} K[1]dK[1]+c_1 e^{y(x)},y(x)\right ] \]

✓ Sympy. Time used: 0.558 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - 2*y(x))*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{2} - W\left (C_{1} e^{- \frac {x}{2} - 1}\right ) - 1 \]