Consider the stochastic differential equation

for all

where is a standard Brownian motion, , and are positive constants. Derive the unique solution to the above SDE.

Apparently this was derived in class but I'm missing that lecture so I guess I wasn't there or have lost it...

The actual solution is...

Anyone got any ideas on how to derive that?

First step is...

I seem to think it involves Ito process/lemmas...

Maybe I should do something like add in...