An RC circuit in series with a voltage source x(t) is represented by a ordinary differential equation

where y(t) is the voltage across the capacitor. Assume y(0) is the initial voltage across the capacitor.

(a) If it is known that the resistor has a resistance R, and the capacitor C = 1 F. Draw the circuit that corresponds to the given ordinary differential equation.

(b) For zero initial condition, and x(t) = u(t), is the output of the system

If so, find and plot y(t).

dy(t) dt + 2y(t) = 2x(t) y(t) = e=2 -2t e2* dr? 0.