## Question

###### Using separation of variables method to solve the IBVP Ut=Uxxi 0<x<1 Itbp0 ulo,0)=0=ul1,0) u(x, 0) = 2 sin (Tx) 4(x,,0) = sin (2ux)62produces the general solution ulx,0 = Zsin(nTx)[Ancos(nnt)+B,sin6ntt)]; n =1 Then the solution for the IBVP isOia ulx, t) = sin(Tx) cos(nt) + sin(2 Tx) sin(2nt) TU0 b. ulx,t) = sin(ux) cos(nt) + sin(2 Tx) sin(2nt) 2T 0 â‚¬ ukx, 0) = 2 sin(Ix) cos(nt) + sin(2 Tx) sin(2tt) Old. ulx, t) = sin(Tx) sin(nt) + sin(2 Tx) cos(2nt)ulx; t) = 2sin(Tx) cos(nt) + sin(2 Tx

Using separation of variables method to solve the IBVP Ut=Uxxi 0<x<1 Itbp0 ulo,0)=0=ul1,0) u(x, 0) = 2 sin (Tx) 4(x,,0) = sin (2ux) 62 produces the general solution ulx,0 = Zsin(nTx)[Ancos(nnt)+B,sin6ntt)]; n =1 Then the solution for the IBVP is Oia ulx, t) = sin(Tx) cos(nt) + sin(2 Tx) sin(2nt) TU 0 b. ulx,t) = sin(ux) cos(nt) + sin(2 Tx) sin(2nt) 2T 0 â‚¬ ukx, 0) = 2 sin(Ix) cos(nt) + sin(2 Tx) sin(2tt) Old. ulx, t) = sin(Tx) sin(nt) + sin(2 Tx) cos(2nt) ulx; t) = 2sin(Tx) cos(nt) + sin(2 Tx) sin(2nt) 2T ulx, t) = sin(tx) sin(It) + sin(2 Tx) cos(2nt)

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