Internal problem ID [706]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.7 Mechanical and Electrical Vibrations. page
203
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u=0} \end {gather*} With initial conditions \begin {align*} [u \relax (0) = 0, u^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 20
dsolve([diff(u(t),t$2)+1/4*diff(u(t),t)+2*u(t) = 0,u(0) = 0, D(u)(0) = 2],u(t), singsol=all)
\[ u \relax (t ) = \frac {16 \sqrt {127}\, {\mathrm e}^{-\frac {t}{8}} \sin \left (\frac {\sqrt {127}\, t}{8}\right )}{127} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[{u''[t]+1/4*u'[t]+2*u[t] ==0,{u[0]==0,u'[0]==2}},u[t],t,IncludeSingularSolutions -> True]
\begin{align*} u(t)\to \frac {16 e^{-t/8} \sin \left (\frac {\sqrt {127} t}{8}\right )}{\sqrt {127}} \\ \end{align*}