I don't have much time today, but I can whip out a solution for a).Originally Posted by kingkaisai2
Since thus where x is a constant.
So where k and x are constant.
The general solution of such a linear differential equation is of the form
Plugging these into your differential equation gives:
Comparison shows that .
So far we have:
Now, we know that the maximum charge on the battery is Q. Thus the limit of q(t) as t goes to infinity is Q. Note that b is a negative number (given the range of acceptable x values.) Thus the limit of the exponential function as t gets very large is 1. ie.
Thus and we know according to the problem statement. Thus A = Q and your final solution is: