  For every commutative differential algebra one can define the Lie algebra of
special derivations.
  It is known for years that not every Lie algebra can be embedded to the Lie
algebra of special derivations of some differential algebra.
  More precisely, the Lie algebra of special derivations of a commutative
algebra always satisfy the standard Lie identity of degree $5$.
  The problem of existence of such embedding is a long-standing problem (see
\cite{YuPSt5,PoinsotAAM,Poinsot}), which is closely related to the Lie algebra
of vector fields on the affine line (see \cite{YuPSt5}).
  It was solved by Razmyslov in \cite{YuPSt5} for simple Lie algebras
satisfying this identity (see also \cite[Th. 16]{Poinsot}).
  We extend this result to prime (and semiprime) Lie algebras over a field of
zero characteristic satisfying the standard Lie identity of degree~$5$.
  As an application, we prove that for any semiprime Lie algebra the standard
identity $St_5$ implies all other identities of the Lie algebra of polynomial
vector fields on the affine line.
  We also generalize some previous results about primeness of the Lie algebra
of special derivations of a prime differential algebra to the case of
non-unitary differential algebra.
