How do you know where to start when solving SDE question? in this case, why Let Xt = Ut exp (-gamma t) ? Thanks
The general form of dX(t) = -gamma * X(t) * dt has solution: constant * exp[-gamma * t], so the answer makes an educated guess as to the form of the solution for the equation in question. It's explained in a bit more detail in the section on the Ornstein-Uhlenbeck process in the stochastic calculus chapter. You could also look on wikipedia for "examples of differential equations" to find more info on solving them (I've brushed up a bit today).
