Finding the solution to a non-homogeneous matrix exponential. – math.stackexchange.com

Consider $$\frac{d}{du} \begin{bmatrix}a\\b \end{bmatrix} = \begin{bmatrix}-x& y\\ -y&-x\end{bmatrix} \begin{bmatrix}a\\ b\end{bmatrix} + \begin{bmatrix}\cos(zu)\\ -\sin(zu)\end{bmatrix}$$ ...

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