67.18.1 problem 27.1 (a)

Internal problem ID [16872]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.1 (a)
Date solved : Thursday, October 02, 2025 at 01:40:00 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 10

ode:=diff(y(t),t)+4*y(t) = 0; 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 3 \,{\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 12

ode=D[y[t],t]+4*y[t]==0; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 3 e^{-4 t} \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = 3 e^{- 4 t} \]