74.19.9 problem 9

Internal problem ID [16631]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 5. Applications of Higher Order Equations. Exercises 5.1, page 232
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 09:13:29 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&={\frac {1}{3}}\\ x^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+9*x(t)=0,x(0) = 1/3, D(x)(0) = -1],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

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

\[ x(t)\to \frac {1}{3} (\cos (3 t)-\sin (3 t)) \]