I have never done this one...and I am not completely sure how to do this, but I have a few quick notions that you may want to follow

A) Use Leibniz's rule of differentiation and see if this turns into a simple ODE

B) This looks like prime countour integral to me

C) Rewrite it as

and complete the square. I will try this if I get time and get back to you if none of the other members do.

Best of luck