GATE EC 2026 Set 1 Q13 — Circuit Analysis

The relation between the input current ( $I$ ) and the output voltage ( $V$ ) of a circuit is governed by the equation: $C \dfrac{d V}{d t}=I(t)-m(t)$. The circuit is excited by $I(t)=q \delta(t)$, where $q$ is a real valued constant. $V$ at $t=0^{-}$is $V_{0}$.

Which of the following is an equivalent representation of the above case?