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Solve the following partial differential equation using separation of variables method to determine the function 0 (x,t). Sim
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Answer #1

Given PDE is ad = 9th with Bie (%,0) = 0 = 9 (20) ($(0,t) & 0.2 t = f(E) 18 (ort) = (1-at) = g(t) v hat the general solutionSin 20u = 0= sin na 20u = na 7 = 20 forn=0,112 - > d=- We also have => Ġ (x) + M+G(X) = 0 + G(x) = A cose + B sinux G60 - 0.2ی ی مینی & (ort) = f(t) = {on sin nato (fourder sine series) on = 20 { f(t) sin nate at For (3) we can similarly find that ofad En 2 1 (1-2t) sinnat at nat (-4) 199)- 25 de in the east (19*4!) + et *(as ng )/ +2 13 l cos hoté) at ] - - - - - - - - -

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