Chapter 4.7, Problem 9P

In each of Problems 6 through 9, find the solution of the specified initial value problem:

The equation in Problem 5 with initial condition $x\left(0\right)={\left(1,1\right)}^T$

$x\text{'}=\left(\begin{array}{cc}0& 1\\ -1& 0\end{array}\right)x+\left(\begin{array}{l}\cos t\\ -\sin t\end{array}\right)$