Internal problem ID [14895]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+64 x=0} \] With initial conditions \begin {align*} \left [x \left (0\right ) = {\frac {3}{4}}, x^{\prime }\left (0\right ) = -2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+64*x(t)=0,x(0) = 3/4, D(x)(0) = -2],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\sin \left (8 t \right )}{4}+\frac {3 \cos \left (8 t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[{x''[t]+64*x[t]==0,{x[0]==3/4,x'[0]==-2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{4} (3 \cos (8 t)-\sin (8 t)) \]