RL circuit question

l'. Suppose the switch has been in position 1 (connecting the inductor to the battery via resistor R1) for a very long time. Then at time t:0, the switch is changed to position 2 (disconnecting the inductor from the battery and connecting it to the resistor R2) A. B. What is the current through the inductor for t0: Write down KVL for the loop involving L and R2 for t>0 and derive a differential equation relating to the current through the conductor to its derivative. 0'! Recaii that the EMF across an inductor is 3? = L and the d: direction can be determined by Lenz's law) Plug in the ansatz (German word for \"educated guess"): 10) = a + be'\" into this differential equation, and find constants a,b,c that give a solution to the differential equation. (To find a,b consider the value of | at t=0) . Plot the energy stored in the inductor as a function of time (include both tD on your plot, and indicate the values at a few representative times in terms of the variables shown)