85.33.69 problem 70

Internal problem ID [22692]
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 : 70
Date solved : Thursday, October 02, 2025 at 09:10:46 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} \left ({\mathrm e}^{y}+x +3\right ) y^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=(exp(y(x))+x+3)*diff(y(x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {LambertW}\left (\left (x +3\right ) {\mathrm e}^{c_1}\right )-c_1 \]

✓ Mathematica. Time used: 0.113 (sec). Leaf size: 19

ode=(Exp[y[x]]+x+3 )*D[y[x],{x,1}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to W\left (e^{c_1} (x+3)\right )-c_1 \end{align*}

✓ Sympy. Time used: 0.405 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + exp(y(x)) + 3)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + W\left (\left (x + 3\right ) e^{- C_{1}}\right ) \]