How Should You Solve an Inductor Current Problem Using Differential Equations?

[Chunkysalsa]

Homework Statement

Find inductor current for t > 0
http://img192.imageshack.us/img192/5814/unledgo.png
Switch is initially open and closes at t=0+

The professor wants us to solve these only using the Diff Eq approach. On other questions I would just do a KVL with the inductor loop and solves the resultant ODE. However with this one I would have to do a system of equations. I'm not to sure if that's what I'm supposed to do or even how to do that math.

I also tried taking the inductor out and doing a thevenin equivalent. I get the correct time constant this way but the constants of integration are way off.

I really just don't know how to approach this problem.

fyi I'm told the answer is 6 - e^(-t/6) A,whoops sorry for the typo in title, been a tiring day.

 

[Chunkysalsa]

Well since i drew up that schematic to post here I figured I'd run the simulation as well. So I haven't found my error yet but it looks like doing a thevenin equivalent should yield me the correct answer.

Is this the best way to approach this problem though? I still feel like I'm missing some key idea here and my book is absolutely terrible at everything but pretty pictures.EDIT:
Figured out the problem