Suppose that u(x,t) is a C⁽²) solution of the initial/boundary value problem: D.E.uₜ= 5uₓ , 0≤x≤1 ,t≥0, B.C. u(0,t)=u(1,t)=0,t≥0,I.C.u(x,0)=4x(1-x),0≤x≤1.Prove:
a) D'Alembert's solution
b) Duhamel's principle
c) Maximum principle
d) Fundamental solution formula
