# Solving a driven RL circuit with a current source

I was given a practice problem as listed below. It says that the solution is in the form of a second order differential equation, but I thought that only RLC circuits were 2nd order. Am I missing something or is the textbook solution wrong? The values aren't necessarily important as it is the approach. To clarify the value beings solve for is the voltage at some time t ---> v(t).

My attempt:
node 1: 5cos(t) = v(t)/R + L(di/dt)

simulate this circuit – Schematic created using CircuitLab

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• When does the switch close? Are you looking for a solution for the time after the switch closes? – Elliot Alderson Dec 6 at 15:54
• yes, at t=0. I updated the diagram – Jeffery Epenstein Dec 6 at 16:01
• If the switch closes at t=0 then the source no longer has any effect on the circuit. How did you end up with the 5cos(t) in your result? – Elliot Alderson Dec 6 at 23:54