  A construction of differential constraints compatible with partial
differential equations is considered. Certain linear determining equations with
parameters are used to find such differential constraints. They generalize the
classical determining equations used in the search for admissible Lie
operators. As applications of this approach non-linear heat equations and
Gibbons-Tsarev's equation are discussed. We introduce the notion of an
invariant solution under an involutive distribution and give sufficient
conditions for existence of such a solution.
