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g) Consider the problem Ou(x, t) = Oxxu(x, t), u(x,0) = Q(x), 0,u(0,1) = 0,1(L,t) = 0, (x, t) (0, L) x (0,00), T ( [0, LG, te

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doketan o<x<l, tro 4 (21,0) = $200 Ux(0 €) so 4x let) we solve it by sepezutien tion of variable ucm+) = XI ()XT= kxT - I DS KT T+KAT=0 x + x = 0 Boundary conditions gives x(o)=0 =x). Sturm-Liouville BVP we have to solve. X + XCose (1) der? *- <?xco + X: Aett etxe x= x A x_agente xcol = 0 = xre) 9 8 = 0 =B . X(X)=0 &(2,4)=0 trivial soin. we rejecup (x,+) = K2 (3) Tp (4) (akt) Anin e cos (nm) an e erkt cos. (I TTC n=1,2,3,..- ucy.t) = ао co ao +{an eshkt cos ( nita) foInitial condition чгио) - фи) » ф,7) - по Ign (те) where ao &cuada 2 4 а. о = фм) , 2 , - ф») е пnx ). х Б Ena ч 2 х 4 ), Енt 144, z 1 ben²11² n = 1,2 22 n2 11 2 t nint (2 و مانی B is constant مع ولي (e-192²) have h IN I 1 41(4,5) < В 5) E un ca, t)

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