An electric circuit consists of a battery {voltage source] connected to a resistor and capacitor in series. The resulting ordinary differential equation for the voltage on the capacitor limit} is as follows: (HQ: _ v... 1 df _RC_RC .I" 1' in. life will use the values 1 Cl. PinEl Here resistance R is in Dhms. time t is in seconds. capacitance C is in Farads. and voltage Vin is in Volts. Initially. the voltage on the capacitor is zero: rm] = CI. {a} {2 marks] Assume the resistance is constant: R = 1m]. Check by direct sul'Jstitution that the function Vg-{tj = 9(1 e'mf] satises the DDE and the initial condition. {h} {4 marks} Now assume that the resistor slowly degrades. so that its resistance increases with time: R = R\") = III] +2t_ Solve the ordinarg,r differential equation for TIC-[t] with this resistance. using either separation of variables. or the integrating factor method. Make sure to also include the initial condition