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
But I do not think I am on the right path. Could you please help. Thanks for any answer.
