74.19.7 problem 7

Internal problem ID [16629]
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 : 7
Date solved : Tuesday, January 28, 2025 at 09:13:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+16 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=-2\\ x^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+16*x(t)=0,x(0) = -2, D(x)(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\sin \left (4 t \right )}{4}-2 \cos \left (4 t \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 20

DSolve[{D[x[t],{t,2}]+16*x[t]==0,{x[0]==-2,Derivative[1][x][0 ]==1}},x[t],t,IncludeSingularSolutions -> True]
 

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