### Abstract:

A general analytical solution to the one dimensional regular Cauchy
problem of Euler-Poisson-Darboux (EPD) equation has been investigated. The one dimensional EPD which is a Partial Differential Equation (PDE) with initial conditions is transformed into Ordinary Differential Equation (ODE) using Similarity Transformation. The first
derivative of the ODE is eliminated by substitution technique. The coefficient of the first derivative is equated to zero and then solved. The
general solution is a product of two terms. The first term is the one
obtained when the first derivative is eliminated from the ODE and the
second term is the complementary function (cf) obtained from the remaining part of ODE. The arbitrary constants of the cf are obtained
in terms of x and t when the initial conditions are substituted in the
general solution. The general solution is a solution for one dimensional
regular Cauchy EPD’s and degenerate EPD’s, which by coincident are
one dimensional wave equations.