Subject: Re: Integration Constant
Date: Thu 12/24/98 12:23 PM
From: Alex Bogomolny
A word of advice: just integrate dy/dt = ax(0)e-at - b. You can't learn much unless you also do this by hand. After the integration, substitute t=0 and you'll see that indeed c = y(0) + x(0).
As to "t being infinity", the expression is awfully wrong. t is time that can be measured and, therefore, is always finite. It may grow, perhaps, without bound. But this does not mean that it ever will become infinite. Surely, sooner or later, either the first or the second container will become empty. At this point, your equations will cease to make sense, and another set of equations will have to be derived.
All the best,