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When the switch is closed, the inductor conducts current until it becomes DC and the limit is set by R2. So the initial current at t0 is equal to the voltage source divided by the resistor R2.
When the switch opens, the two resistors are in series, so you have effectively one resistor in series with an inductor with some initial current (from above), where this resistor is simply the sum of the two resistances.
So what you end up with is a simple RL circuit where the initial current is known and you (presumably) have to come up with an equation that shows that response.
Some of these initial courses show them the formulas for a number of problems where they can use the the same formula for that somewhat simpler circuit. An example is:
Vc=Vo*(1-e^-t/RC)
They just hand out that formula and show them out to apply it (for example). Im not sure if that's what they are doing here, but then they dont have to get involved with calculus yet. I agree though a full study is better, but sometimes the course is a little simpler than that. I think you know what i mean.
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