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its maximum M at the interior point (x1, tu). Where else U - , 12.9. a) Find the similarity solutions of the equation ut - UaPlease provide an answer with a clear typing( especially if it is a handwriting please be careful to make it readable) and step by step solutions for both part a and part b. Thanks in advance

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2.99 Uta uxr, 2GR, to lef. u(xit) = f(2) where not So by there substitution in l weget l.fo du zuch integrating, af en comprato Say) & an an 22 - 200 512 2 azt a 112 m o nat de = u(xit) & G & cal é o Now dr. m. ert (1e). .Ut - U22 = 0 270 to, U10,K) = , tyo u(ait) – o as and to ucno 0 20 470 Here we use tourier sine s(u(ait) - U(d, t) transformU (e,t) eart = 2 & eart + (66) Now Now U (8,0) = 2 + C. (d) one t (6) Tas 0(0,0) =0 (6) = - Pra FIU (8,0)=07 Uldit) = [ 2 edt

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