RLC Circuit and a Non-homogenous Diff EQ

Hi there everyone -

My first post on her, so a little intro is necessary I think...

I 'm 30 and have a degree in Physics. I dropped out of my PhD many years ago and am now trying to reteach myself my math and physics so as to try and get into a PhD program here in the US (I originally from Scotland). Unfortunately, I seem to have forgotten a lot of this stuff, so I have problems with things now and then - here is a question from 'Advanced Engineering Mathematics' By Kreyzig...

Assume a RLC circuit where R=0. If the driving EMF E(t) has a jump of magnitude J at t=a, then show that dI/dt has a jump of magnitude J/L at t=a while I(t) is continuous at t=a.

My thoughts - I started by setting up the standard 2nd Order Diff Eq and setting it equal to 0 for t<a and J for t>=a. However, since the additional term to the general solution (the particular solution) is independent of time under those circumstances, there is no change to dI/dt - the graph is essentially a step function. I think I may be misinterpreting the question, but I can't think of any other way to read this...

HELP!

Thanks everyone :D