Are the subrings $\mathbb{C}\lbrack t^2,t^3\rbrack$ and $\mathbb{C}\lbrack t^3+3t^2,t^2+2t\rbrack$ of $\mathbb{C}\lbrack t\rbrack$ isomorphic? I do not think that they are, but I was not able to prove it.
My attempt was focused on comparing their integral closures, but I was not quite able to derive the integral closure of $\mathbb{C}\lbrack t^3+3t^2,t^2+2t\rbrack$.