Chapter 3.7, Problem 29P

(a)

To determine

The solution of the initial value problem $u^{″}+\frac{1}{4}{u}^{\prime }+2u=0$, $u\left(0\right)=0,u^{\prime }\left(0\right)=2$.

(b)

To determine

To sketch: The graphs of solution curve $u\left(t\right)$ and its derivative on same axis.

(c)

To determine

To sketch: The graph of $u^{\prime }\left(t\right)$ versus $u\left(t\right)$ and find its direction.