I'm trying to find an expression for the current i(t) as a function of C and V_out (t) after t = 0. I have an answer but still not sure at all if its correct or not.

Here is my answer:

I know that

i(t) = C*dV(t) / dt

V(t) = Ri(t) + V_out (t)

combining them together

i(t) = C-dV_out(t)/dt - dV_out(t) / R

Here is the circuit.

Thanks