Find particular solutions to the heat equation on a rod x 2 [0; 2p], with d = 4, with insulated endpoints given the following initial conditions: (a) f (x) = 1+cos 3 2 x . (b) f (x) = 3+cos 12 x +cos(2x). (c) f (x) = 2+å¥n=1 1 n2 cos(nx). (d) f (x) = å¥ n=1 1 (2n)2 cos(nx). (e) f (x) = x.

a

step-by-step explanation:

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)

well since the real answer is 8.9 i guess the estimation would be 9