See attached file.
Verify that (6-85a) and (6-85b) are solutions to (6-84a).
Equation 6-85a represents an outwardly (in the radial direction) traveling wave and (6-85b) describes an inwardly traveling wave, assuming time variations.
It verifies that the traveling wave equations are solution to a differential equation. The solution is detailed and was rated '5/5' by the student who posted the question originally.