Nonsigular curve of degree $3$ in $\mathbb P^2$ over a field of characteristic $3$

Question

I am trying to do problem $1.5.5$ from Algebraic Geometry by Robin Hartshorne. The problem states:

For every degree $d>0$, and every $p=0$ or a prime number, give the equation of a nonsingular curve of degree $d$ in $\mathbb{P^{2}}$ over a field of characteristic $p$.

I have polynomials that work for every case except for the case where $p=d=3$ .I have tried several different polynomials of degree $3,$ but they always seems to have a singular point.Any help/ hint would be greatly appreciated.