In a linear algebra exam I can across the following question.
Determine the general solution of the differential equations $$ \begin{pmatrix} \dot x_{n+1}\\ \dot y_{n+1}\\ \dot z_{n+1} \end{pmatrix}= \begin{pmatrix} 6&3&3\\ 3&6&3\\ 3&3&6 \end{pmatrix} \begin{pmatrix} x_{n}\\ y_{n}\\ z_{n} \end{pmatrix}. $$
Now in class, we'd previously seen how to solve DEs and recurrence relations using diagonalisation, however I've never seen a problem which was both a DE and a recurrence relation.
How does one even interpret the problem, notationally speaking? I think it means that the derivative of the $(n+1)$st vector is given by the product of the matrix with the previous vector. So presumably one would first have to solve it as a DE, then as a recurrence relation? Or the other way around?