Ok. This is a crash course on ODE's: first line of attack: separation of variables. Can you get all the

's on one side, and all the

's on the other? In this case, you can. You obtain, by using multiplication of differentials:

.

What you do then is integrate both sides. I would use the definite integral, so that you can more easily take into account the initial conditions:

,

where I've used the dummy variables

and

to avoid confusion. At least, I hope I've avoided confusion.

In performing the integration on the LHS, you're going to get a rather messy expression. You may not be able to solve it explicitly for

. That may or may not be a severe drawback, depending on what you want to do with the equation.

Reply to AllanCuz: What would your variable

be representing?