$$\frac{d}{du} \begin{bmatrix}a\\b \end{bmatrix} = \begin{bmatrix}-x& y\\ -y&-x\end{bmatrix} \begin{bmatrix}a\\ b\end{bmatrix} + \begin{bmatrix}cos(zu)\\ -sin(zu)\end{bmatrix}$$
P = $\begin{bmatrix}-x& y\\ -y&-x\end{bmatrix}$
And I have for u=0: $\begin{bmatrix}a\\b \end{bmatrix} = \begin{bmatrix}0\\0 \end{bmatrix}$
Having proved that ePu = e-xu $\begin{bmatrix}cos(yu)& sin(yu)\\ -sin(yu) & cos(yu)\end{bmatrix}$
My question is - how do I use this proof to solve this problem using the initial conditions.
Having thought about it - I consider that using the double angle formulae may help althought I haven't been able to formulate this.
Any help would be welcome.