A circuit consists of an ideal battery of constant electromotive force \(\mathcal{E}\), a resistor of resistance \(R\), an open switch, and an uncharged non-linear capacitor connected in series. The capacitance of the capacitor depends on the potential difference \(V\) across its plates according to \(C(V) = C_0\left(1 + \dfrac{V}{\mathcal{E}}\right)\), where \(C_0\) is a positive constant. The switch is closed at time \(t = 0\). Which of the following expressions correctly gives the rate of change of the potential difference across the capacitor, \(\dfrac{dV}{dt}\), as a function of \(V\)?