74.11.53 problem 62 (d)

Internal problem ID [16224]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (d)
Date solved : Thursday, March 13, 2025 at 07:59:26 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 12

ode:=diff(y(t),t)+4*y(t) = exp(-4*t); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left (t +1\right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 14

ode=D[y[t],t]+4*y[t]==Exp[-4*t]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-4 t} (t+1) \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + Derivative(y(t), t) - exp(-4*t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (t + 1\right ) e^{- 4 t} \]