An ideal LC circuit consists of an inductor with self-inductance \(L\) connected to a parallel-plate capacitor with plate area \(A\). An external mechanism pulls the capacitor plates apart such that the plate separation increases linearly with time according to \(d(t) = d_0 (1 + \alpha t)\), where \(d_0\) and \(\alpha\) are positive constants. Let \(C_0 = \dfrac{\varepsilon_0 A}{d_0}\) represent the capacitance at time \(t = 0\). Assuming electrostatic and magnetostatic approximations hold throughout the motion, which of the following differential equations correctly describes the charge \(q(t)\) on the capacitor as a function of time \(t\)?