This looks to be a differential equations problem. You've got and you want to find . This is a separable equation which can be solved by taking and integrating both sides. The fact that when t = 0, x = 1 gives you an initial condition. The problem is that integral on the left hand side is pretty nasty. I'm not sure that you'll be able to solve for x after all is said and done. Maybe see if someone on the differential equations board can figure this out.