The voltage across the capacitor in a driven RC-circuit is modeled by the initial value problem V′c + Vc = cos(t), Vc(0) = 0. The solution of the problem can be written Vc = Vt + Vs, where

The solution Vs is called the steady-state solution and the solution Vt is called the transient solution. On one plot, sketch the solutions Vs, Vt, and Vc in blue, red, and black, respectively, over the time interval [0,6π], Add a legend to your plot.
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