7.18.1 problem 1

Internal problem ID [530]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 1
Date solved : Wednesday, February 05, 2025 at 03:42:19 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=5\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.238 (sec). Leaf size: 10

dsolve([diff(x(t),t$2)+4*x(t)=0,x(0) = 5, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = 5 \cos \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 11

DSolve[{D[x[t],{t,2}]+4*x[t]==0,{x[0]==5,Derivative[1][x][0] ==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 5 \cos (2 t) \]