38.5.3 problem 3

Internal problem ID [8351]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 05:29:33 PM
CAS classification : [_quadrature]

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=1+exp(3*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-3 x}}{3}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 12

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

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