Question: Please use PDE(partial differential equation) content to solve this problem, thank you. The second picture shows problem 2. The third picture shows (1) and (2)

Please use PDE(partial differential equation) content to solve this problem, thank you.

The second picture shows problem 2.

The third picture shows (1) and (2) in case if you need it.

Please use PDE(partial differential equation)

This exam is aimed at solving the PDE ut = Kuxx + Mux, where k, MER, K > O u(xx, 0) = $(2) 1242 offs) ban (1) call 1.a. Prove the shift property for the Inverse Fourier Transform f ( w - c ) = eicc f ( w)2. Use (1) and (2) to show that at = - kwu + inwi and u( w, 0 ) = $ ( w ).3. For a given w, solve the ODE in problem 2. to prove that i ( w ) = p(w) e-kwattiput

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