44.3.15 problem 2(e)

Internal problem ID [9125]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 2(e)
Date solved : Tuesday, September 30, 2025 at 06:04:45 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 17

ode:=diff(y(x),x)+4*y(x) = exp(-x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 21

ode=D[y[x],x]+4*y[x]==Exp[-x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{-4 x} \left (e^{3 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 17

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

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