74.19.8 problem 8

Internal problem ID [16630]
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 : 8
Date solved : Tuesday, January 28, 2025 at 09:13:25 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+256 x&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

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

dsolve([diff(x(t),t$2)+256*x(t)=0,x(0) = 2, D(x)(0) = 4],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\sin \left (16 t \right )}{4}+2 \cos \left (16 t \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 20

DSolve[{D[x[t],{t,2}]+256*x[t]==0,{x[0]==2,Derivative[1][x][0 ]==4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} (\sin (16 t)+8 \cos (16 t)) \]