Let \(R\subset A\) be factorial domains containing \(\mathbb Q\). In the paper under review the authors give an equivalent condition in terms of locally nilpotent derivations for \(A\) to be \(R\)-isomorphic to \(R[v,w]/(cw-h(v))\), where \(0\not=c\in R\) is not a unit and \(h(v)\in R[v]\) is nonconstant modulo every prime factor of \(c\): There exists an irreducible locally nilpotent \(R\)-derivation \(\xi\) of \(A\) with ring of constants \(A^{\xi}\) equal to \(R\) and such that there exists \(c=\xi(s)\in{\mathfrak p}{\mathfrak l}=\xi(A)\cap A^{\xi}\) with the property that the ideal \(R[s]\cap cA\) of \(R[s]\) is generated by \(c\) and a polynomial \(h(s)\in R[s]\). The result implies the isomorphism of the differential rings \((A,\xi)\) and \((R[v,w]/(cw-h(v)),\delta)\) where \(\delta(v)=c\) and \(\delta(w)=\partial_vh(v)\). The authors show that an example from a paper by Daigle gives that the result does not hold if \(A\) in not factorial. In the particular case when \(R\) is a polynomial ring in one variable, the result yields a natural generalization of of a result in Masuda characterizing Danielewski hypersurfaces whose coordinate ring is factorial. Finally, the authors apply their result to the study of triangularizable locally nilpotent \(R\)-derivations of the polynomial ring in two variables over \(R\).