38.1.54 problem 68

Internal problem ID [8215]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 68
Date solved : Tuesday, September 30, 2025 at 05:18:56 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=5-y \end{align*}

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

ode:=diff(y(x),x) = 5-y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 5+{\mathrm e}^{-x} c_1 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 20

ode=D[y[x],x]==5-y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5+c_1 e^{-x}\\ y(x)&\to 5 \end{align*}

✓ Sympy. Time used: 0.065 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), x) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + 5 \]