## Equilibrium temperature distribution [closed]

Determine the equilibrium temperature distribution, if it exists, for each of the folowing problems. Specify values/ranges for A if necessary.

$\frac{\partial u}{\partial t} = \frac{\partial^2u}{\partial x^2}$ with $u(x,0)=f(x), \frac{\partial u}{\partial x}(0,t) = 1$ and $\frac{\partial L}{\partial x}(L,t) = A$

My solution is $0=\frac{d^2u}{d x^2}$

c1=$\frac{du}{dx}$

c1x+c2=u(x)

$\frac{du}{dx}$(0,t)=c1=1

$\frac{du}{dx}$(L,t)=c1=A

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