inductor resistor differential equation
I think you started by using the current divider formula to find the current in the inductor, but no part of it is correct. To use that formula you would need to find the impedance of each parallel path as well as the total impedance. It doesn't look like you've done that, and it's an unnecessarily complicated way to go anyway.

Instead, consider the two scenarios: t&lt;0 and t&gt;0.

For t&lt;0 the current is constant. For constant current the impedance of an inductor is zero. So all the current (4mA) is flowing through the inductor. That scenario is now done.

For t&gt;0 the current source goes to zero. With no current in the current source branch, the circuit reduces to just two elements: L1 and R2. You then just need the inductor formula:

\$v_{L1} = L1 * \frac{di_{L1}}{dt}\$

And the resistor formula:

\$v_{R2} = R2 * i_{R2}\$

Since the voltage across the two elements must sum to zero, and the current flowing through them is the same, the two equations combine:

\$L1 * \frac{di_{L1}}{dt} = - R2 * i_{L1}\$

Which is a differential equation that probably looks a lot more familiar.