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Problem 10. (10 bonus pts) Let n 2 1. For x E R, t > 0, show that ux = 1 1 2 / 2

Problem 10. (10 bonus pts) Let n 2 1. For x E R", t > 0, show that ux = 1 1 2 / 2 1 tn/2 e 4t tn/2 e 4t is a solution of ut = Au = Unix + . . . + Uxnan. Then find the integral Son u(x)dx. (You must justify your answer.)

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