Integration of PDEs via C∞-structures

Following classical method of differential constraints, interpreted in jet space, we present a constructive procedure for the integration of partial differential equations (PDEs). The approach consists of adjoining compatible auxiliary equations to reduce the PDE to a finitetype system in which the Vessiot distribution becomes involutive on an open set. Rather than classical solvable structures, we employ C∞-structures of distributions, a generalization with relaxed bracket conditions that are systematically easier to construct, yet still guarantee integration through successive Pfaffian equations. Three explicit examples illustrate the method: the linear wave equation with affine constraints, the Liouville equation, and a non-trivial rational nonlinear PDE. In every case the procedure yields an explicit family of solutions.