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**Aryth** Find the Steady State Solution and state the Transient Problem.

$\displaystyle u_t = ku_{xx}$

$\displaystyle 0 < x < L$

$\displaystyle t > 0$

Initial Condition: $\displaystyle u(x,0) = f(x)$

a) Boundary Conditions:

$\displaystyle u_x(0,t) = 0$

$\displaystyle u_x(L,t) = -1$

b) Boundary Conditions:

$\displaystyle -u_x(0,t) + \frac{1}{2}u(0,t) = 0$

$\displaystyle -u_x(L,t) - \frac{1}{2}u(L,t) = 1$

I've handled conditions of the first kind, u(x,t) = c. But I have not dealt with either of these before. Any help would be appreciated.