Internal problem ID [14900]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+256 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 2, x^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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: 0.015 (sec). Leaf size: 20
DSolve[{x''[t]+256*x[t]==0,{x[0]==2,x'[0]==4}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{4} (\sin (16 t)+8 \cos (16 t)) \]