Determine the covariance function for the response \left\{X\left(t\right) \right\} of a linear system described by c \dot X\left(t\right) +kX\left(t\right) =F\left(t\right) with X\left(0\right) =0 . For t\gt 0 , \left\{F\left(t\right) \right\} is a mean-zero, nonstationary delta-correlated process with
\phi _{FF}(t_{1},t_{2})=G_{0}(1-e^{-at_{1}})\delta \left(t_{1}-t_{2}\right)