3. Consider the (dispersive) wave equation ди =удхаи, where everything is real. a) Find the family of plane wave solutions of the form u(x,t;k) exp[i(kx-w(k)t)] b) Find the "dispersion relation", the "phase velocity" and the "group velocity" for this family of plane waves. c) Use these objects (dispersion relation, phase velocity, group velocity, and Fourier representation) to describe, qualitatively, the behavior of the solution of the initial value problem for this equation as t→ infinity.