Question

Problem #8: A rod of length 9 coincides with the interval [0,9] on the x-axis. Consider the heat equation in the special case when k=1 if both ends are held at temperature zero for all t> 0. The initial temperature is f(x) throughout where f(x) = a sin(876x) + b sin(4x) The solution to the heat equation under the above conditions is of the form u (x, t) = a g1(x, t) + b g2(x, t) (a) Enter the function gi(x, t) into the answer box below. (b) Enter the function g2(x, t) into the answer box below. Problem #8(a): Enter your answer as a symbolic function of x,t, as in these examples Problem 8(b): Enter your answer as a symbolic function of x,t, as in these examples Just Save Submit Problem #8 for Grading Problem #8 Attempt #1 Your Answer: 8(a) 8(b) Your Mark: 8(a) 8(b) Attempt #2 8(a) 8(b) 8(a) 8(b) Attempt #3 8(a) 8(b) 8(a) 8(b) Attempt #4 8(a) 8(b) 8(a) 8(b) Attempt #5 8(a) 8(b) 8(a) 8(b)

Answer 1

given U 08, +) = ago 66, t) +b $ (3,+) foe) a Sin BTX) + Sin (473) R=1 L=9 general Solution of heat equation urt) An sin(n) + nel at user t) = E An An sin (MA) 81 nol u (x,0) = foc) *o a Sin(BAX) + sin gax) = Ë An Sinans se ni a sin egtx) + b sin(974) E An Sin inase 9 nal a sin(84) + b Singap) = Azg Sin (893) + 136 Sintant) t A12 a A 36 = b 361 For es * + b Sin(44%) e 16x9 useit) = a sin(87x) e -64744 UGGE) = a Sin(8m2) e + b Sin (47x) e ux. t) = a J.CX:+) + b (kit) 6474 dickit) = sing wis die a - 1674 Dy68+) = sin(4ack).