In this problem, $x=c_{1}cos(t)+c_{2}sin(t)$ is a two$-$parameter family of solutions of the second$-$order $DE{x}^{\text{'}\text{'}}+x=0.$

$x(\frac{}{3})=\frac{\sqrt[\phantom{2}]{3}}{2},x^{\text{'}}(\frac{}{3})=0$

Substitute the initial value $t=\frac{}{3}$ to find the initial conditions in terms of $c_1$ and $c_2.$

$x(\frac{}{3})=$

$x^{\text{'}}(\frac{}{3})=$

Find a solution of the second$-$order IVP consisting of this differential equation and the given initial conditions.