Analytic approach for homogeneous and non-homogeneous second order PDE's with an analytical solution of Navier Stokes Equations on ${\mathbb{R}}^3$ for a viscous incompressible fluid

Under this method second order \textbf{partial differential equations (PDE’s)} can be reduce to first order PDE’s, simplifying the Initial value problem $\mathbf{\text{IVP}}$ or Border value Problem $\mathbf{\text{BVP}}$ for most cases of second-order differential equation, letting easiest proofs for existence and uniqueness of the PVI and BVP problems.