First of all I would (just for convenience) rewrite Q(t) as .
Secondly, where i is current.
Also, have you assumed that Q(0) = 0?, because, as I understand, since and and C is constant, there are charges involved from the beggining (the capacitor is storing that charge eventually).
The problem also states that the capacitor is discharging so the charges are moving (which means that ).
As for the constants, I would get Q from (2) and replace it in (1). There we have our first equation. For the second one I would replace (1) in the differential equation and that seems to be solvable.
Finally, the current will be a time function.
As an engineering student, I'd approach it that way. Hope it helps.