39.5.15 problem Problem 24.44

Internal problem ID [6557]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.44
Date solved : Wednesday, March 05, 2025 at 12:56:35 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-2 \end{align*}

✓ Maple. Time used: 0.171 (sec). Leaf size: 13

ode:=diff(diff(x(t),t),t)+4*diff(x(t),t)+4*x(t) = 0; 
ic:=x(0) = 2, D(x)(0) = -2; 
dsolve([ode,ic],x(t),method='laplace');
 

\[ x \left (t \right ) = 2 \left (t +1\right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 47

ode=D[x[t],{t,2}]+3*D[x[t],t]+4*x[t]==0; 
ic={x[0]==2,Derivative[1][x][0 ]==-2}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {2}{7} e^{-3 t/2} \left (\sqrt {7} \sin \left (\frac {\sqrt {7} t}{2}\right )+7 \cos \left (\frac {\sqrt {7} t}{2}\right )\right ) \]

✓ Sympy. Time used: 0.200 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(4*x(t) + 4*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 2, Subs(Derivative(x(t), t), t, 0): -2} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (2 t + 2\right ) e^{- 2 t} \]