Write the following boundary value problem as a system of ordinary differential equations Ut=3uzz 0 0 u(0, t) = u(5, t) = Choose the correct answer from the alternatives below. Select one: X' + XX=0 - ?x=0) 3 T'-3AT=0 where X(0) = X(5) = 0 O T' - 3AT = 0 X" -AX= 0 alternatively T AT 0 X" where X(0) -X(5) 0
Select one: O If X" - XX=0 subject to the initial conditions X(0) X(27) = 0 then determine the non-trivial solution for ? = (12) for n 1, 2, 3,... = Xn (1) = An cos None of the alternatives are correct Xn (r) = An sin (not) for n 1, 2, 3,... 2 X? (x) = An cos ( (172 for n 1, 2, 3, . . . X?(x) = An sin ¹ (127) for n 1, 2, 3,... = K