Internal problem ID [4653]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {\frac {x^{\prime \prime }}{2}+48 x=0} \end {gather*} With initial conditions \begin {align*} \left [x \relax (0) = {\frac {1}{6}}, x^{\prime }\relax (0) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ x \relax (t ) = \frac {\cos \left (4 \sqrt {6}\, t \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 18
DSolve[{1/2*x''[t]==-48*x[t],{x[0]==1/6,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{6} \cos \left (4 \sqrt {6} t\right ) \\ \end{align*}