How to numerically solve a differential equation which is a function of voltage and not a function of time

working on an Double layer capacitor, it can be simplified as a series RC circuit. The tricky part is that the capacitance in this Double layer capacitance is not constant and changes according to the applied voltage. The differential equation starting from Q=C*V turns out to be as attached in the png.

How can we analyse or numerically solve this D.E and analyse the relation between input voltage and the capacitance.

I shall be highly grateful to you for the help.

[Torsten]

I see three time-dependent functions (Vi(t), Vc(t) and i(t)), but only one equation. So two of the three unknown functions must either be known or there must exist additional equations to solve for them. Can you share these functions or equations ?

[Ali Zahid]

i(t) can be calculated as simple equation V = I*R . I(t)will be input voltage - Capacitor voltage / Resistance. we can know what input voltage we shall be supplying the we can measure the voltage at the entry and exit of the resistor and then simple subtraction to get the resistor voltage which can be divided by the resistance if i am not wrong