I have the following 4 governing equations

i) V1(t) = a.Id(t)^2 + Rd.Id(t)

ii) V1(t) = V(t) - R.I(t)

iii) Ic(t)= C.dV(t)/dt

iv) I(t) = Ic(t) + Id(t)

The values of a, Rd, R and C are constant.

And I need to find an equation in terms of V on the LHS and I on the RHS, but no matter how I look at it I can't find a solution. I've been two days looking at this and I must be missing something. everytime I try to solve it I start to get terms which are the product of I or dI/dt and V or dV/dt