Question $8.$ A circuit comprises a resistor $R$ in series with a capacitor $C.$ It is initially in a steady state with an applied voltage of $V_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}.$ At time $t=0$ the applied voltage is suddenly changed to $V_{\text{f}\text{i}\text{n}\text{a}\text{l}}$ as shown in the circuit below.

Construct the differential equation for the voltage on the capacitor $v_C(t)$ during the resultant transient. Confirm that the result is the general rule for first$-$order transients,

$v_C(t)=V_{\text{f}\text{i}\text{n}\text{a}\text{l}}+(V_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}-V_{\text{f}\text{i}\text{n}\text{a}\text{l}})exp(-\frac{t}{})$

I am not sure how to make the set up equations for t t right after $0$ and t aproaching infinity