74.19.2 problem 2

Internal problem ID [16624]
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 : 2
Date solved : Tuesday, January 28, 2025 at 09:13:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 x^{\prime \prime }+4 x&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

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

dsolve([9*diff(x(t),t$2)+4*x(t)=0,x(0) = -1/2, D(x)(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {3 \sin \left (\frac {2 t}{3}\right )}{2}-\frac {\cos \left (\frac {2 t}{3}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 26

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

\[ x(t)\to \frac {1}{2} \left (3 \sin \left (\frac {2 t}{3}\right )-\cos \left (\frac {2 t}{3}\right )\right ) \]