#### little_ja-o

##### New member

- Joined
- Jun 30, 2006

- Messages
- 3

equation ut − Duxx − u = 0. First show that the equation separates and

find the general solution for X(x) and T(t). Next, assuming that D > 0, >= 0, L > 0, solve the boundary value problem

ut − Duxx − u = 0 for all 0 <= x <= L, t >= 0

u(0, t) = u(L, t) = 0, for all t >= 0 (1)

u(x, 0) = sin((pi)x/L) + sin(2(pi)x/L).

Finally characterise the difference between the solutions for > D(pi)^2/L^2 and

< D(pi)^2/L^2.