a question about circuits and diferential equation Consider the DC circuit of Figure $ 4$. Inductance L satisfies $L = (R^2) C / 2$. Calculate:
a) The differential equation for the charge $ Q (t) $ contained in the capacitor;
b) The solution of diferential equation of the preceding item;
c) the power dissipated in the resistance and the energy stored in the capacitor for sufficiently long times so that only the stationary solution is present.

I am going to give you a sketch on how you can find the solution. 
As I stated in the comments, notice that this is not an RLC circuit, because C and L are in parallel whereas they are in series in an RLC circuit.
Since C and L are in parallel, we have
$$v_C(t) = v_L(t)$$
and
$$i(t) = i_R(t) = i_L(t) + i_C(t)$$
From Kirchhoff's voltage law:
$$v_R(t)+v_L(t) = v_R(t)+v_C(t) = -\epsilon$$
Moreover,
$$v_L(t) = L \frac{di_L(t)}{dt}$$
and
$$ v_C(t) = \frac {Q(t)}{C} = \frac 1 C \int_{-\infty}^{t} i_C(\tau) d \tau$$
This is all you need to solve the problem.
