A new differential identity is obtained for a scalar function u(x, y) dependent on two independent variables as a result of research of the set of differential invariants of a group G of point transformations. The identity implies some integral identities and formulas useful for deriving some functionals in inverse problems for certain classical differential equations of mathematical physics. In particular, the formulas establish relations between certain integral medium characteristics (the parameter n(x, y) in the wave equation) and the wave process (the solution u(x, y, t) of the corresponding direct problem for these equations).