  Given a weight of sl(n), we derive a system of variable-coefficient
second-order linear partial differential equations that determines the singular
vectors in the corresponding Verma module. Moreover, we completely solve the
system in a certain space of power series. The polynomial solutions correspond
to the singular vectors in the Verma module. The well-known results of Verma,
Bernstein-Gel'fand-Gel'fand and Jantzen for the case of $sl(n)$ are naturally
included in our almost elementary approach of partial differential equations.
