Internal problem ID [705]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {u^{\prime \prime }+2 u=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(diff(u(t),t$2)+2*u(t) = 0,u(t), singsol=all)
\[ u \relax (t ) = c_{1} \sin \left (t \sqrt {2}\right )+c_{2} \cos \left (t \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[u''[t]+2*u[t] ==0,u[t],t,IncludeSingularSolutions -> True]
\begin{align*} u(t)\to c_1 \cos \left (\sqrt {2} t\right )+c_2 \sin \left (\sqrt {2} t\right ) \\ \end{align*}