32.4.18 problem 19

Internal problem ID [7791]
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 : Tuesday, September 30, 2025 at 05:05:30 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*}

✓ Maple. Time used: 0.071 (sec). Leaf size: 13

ode:=1/2*diff(diff(x(t),t),t) = -48*x(t); 
ic:=[x(0) = 1/6, D(x)(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

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

\begin{align*} x(t)&\to \frac {1}{6} \cos \left (4 \sqrt {6} t\right ) \end{align*}

✓ Sympy. Time used: 0.042 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(48*x(t) + Derivative(x(t), (t, 2))/2,0) 
ics = {x(0): 1/6, Subs(Derivative(x(t), t), t, 0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

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