Problem 1) part (A): 1: Find the 2x- periodic solution u(t, x) to дти = Чихх u (0,x) = 5 cos (3x) - 2 sin (2x) +4 part (B): Find the solution u(t, x) to ди= бихх u(€, 0) = u(t, 10)=0 t> 0, XER XERR u(0,x) = -2 sin ( 3xx ) + b sin (5TX) + 5 sin ( 6xx) 10 : part (C) Find the solution u(t,x) to 764 = 24xx ux (t, 0) = ux (t, 1) = 0 u (o, x ) = -2 + 4 cs (TX) - 765 (12xx) t70, 06x-10 t>o 00, 0

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