85.33.27 problem 27

Internal problem ID [22650]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 27
Date solved : Thursday, October 02, 2025 at 09:02:43 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

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

ode:=(x+y(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: 0.011 (sec). Leaf size: 24

ode=(x+y[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: 0.363 (sec). Leaf size: 17

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)
 

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