38.6.4 problem 4

Internal problem ID [8434]
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 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 05:36:41 PM
CAS classification : [_quadrature]

\begin{align*} 3 y^{\prime }+12 y&=4 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=3*diff(y(x),x)+12*y(x) = 4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{3}+{\mathrm e}^{-4 x} c_1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 24

ode=D[y[x],x]+12*y[x]==4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3}+c_1 e^{-12 x}\\ y(x)&\to \frac {1}{3} \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) + 3*Derivative(y(x), x) - 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 4 x} + \frac {1}{3} \]