Show that the wave function (x) = Ae ikx is a solution of Eq. 40.1 for a

Question:

Show that the wave function ψ(x) = Ae ikx is a solution of Eq. 40.1 for a particle of mass m, in a region where the potential energy is a constant U0 < E. Find an expression for k, and relate it to the particle's momentum and to its de Broglie wavelength.