A resistor R (R = 0.4) and an inductor L (L = 0.08 H) are connected as

Question:

A resistor R (R = 0.4Ω) and an inductor L (L = 0.08 H) are connected as shown. Initially, the switch is connected to point A and there is no current in the circuit. At t = 0 the switch is moved from A to B, so that the resistor and the inductor are connected to Vs (Vs = 6 V), and current starts flowing in the circuit. The switch remains connected to B until the voltage on the resistor reaches 5 V. At that time (tBA) the switch is moved back to A.
The current i in the circuit can be calculated from solving the differential equations:
iR + L di/dt = vs during the time from t = 0 and until the time when the switch is moved back to A.
iR + L di/dt = 0 from the time when the switch is moved back to A and on.
The voltage across the resistor, vR, at any time is given by vR = iR.
(a) Derive an expression for the current i in terms of R, L, Vs, and t for 0 < t < tBA by solving the first differential equation.