In this paper we examine the
question raised by J. F. Ritt in his Colloquium Publication, Differential Algebra
concerning the sludy of the differential ideals generated by the Wronskian. A test for
an element to be a member of a certain (algebraic) ideal is presented and this result
is applied to the differential ideal generated by the Wronskian. All identities of a
certain type of determinant are also obtained.