74.19.3 problem 3

Internal problem ID [16625]
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 : 3
Date solved : Tuesday, January 28, 2025 at 09:13:07 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+64 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&={\frac {3}{4}}\\ x^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+64*x(t)=0,x(0) = 3/4, D(x)(0) = -2],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {\sin \left (8 t \right )}{4}+\frac {3 \cos \left (8 t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 22

DSolve[{D[x[t],{t,2}]+64*x[t]==0,{x[0]==3/4,Derivative[1][x][0 ]==-2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} (3 \cos (8 t)-\sin (8 t)) \]