A first-order differential equation of the form $f\left(t\right)=b\left(dx\text{/}dt\right)+cx$ has a solution of the form $\begin{array}{c}A{e}^{-\frac{t}{\tau }}+\kappa \text{,}\end{array}$ where κ is an arbitrary constant and τ is the time constant of the circuit. What is the general form of the time constant?