7.18.2 problem 2

Internal problem ID [531]
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 : 2
Date solved : Wednesday, February 05, 2025 at 03:42:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+9 x&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=3\\ x^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.205 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+9*x(t)=0,x(0) = 3, D(x)(0) = 4],x(t), singsol=all)
 

\[ x \left (t \right ) = 3 \cos \left (3 t \right )+\frac {4 \sin \left (3 t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[{D[x[t],{t,2}]+9*x[t]==0,{x[0]==3,Derivative[1][x][0] ==4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {4}{3} \sin (3 t)+3 \cos (3 t) \]