Consider again the IVPs shown above.

If \(R\) is time-varying, i.e., \(R(t)\), then show that the solution can be formally written in terms of the exponential matrix as

\[\boldsymbol{y}=\exp (\tilde{A} t) \boldsymbol{y}_{0}+\int_{0}^{t} \exp [-\tilde{A}(\tau-t)] R(\tau) d \tau\]

where \(\tau\) is the dummy variable for integration purposes.

This formula is useful for the case of a time-varying stimulus. You may want to write a MATLAB code to implement this and test it on a benchmark problem.