38.4.18 problem 19

Internal problem ID [6504]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:09:24 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \frac {x^{\prime \prime }}{2}&=-48 x \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&={\frac {1}{6}}\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 13

dsolve([1/2*diff(x(t),t$2)=-48*x(t),x(0) = 1/6, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\cos \left (4 \sqrt {6}\, t \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 18

DSolve[{1/2*D[x[t],{t,2}]==-48*x[t],{x[0]==1/6,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{6} \cos \left (4 \sqrt {6} t\right ) \]