sara

My heat flow equation is

$$ u_t=4u_{xx}+4$$

And my boundary conditions are

$$u(0,t)=-2$$ and $$u(1,t)=5$$ when $u_t=0$, solving for $u_{xx}$ gives us $u_{xx}=-1$.

Integrating twice, we get

$$u(x) = -x^2+ax+b$$

By using our initial conditions we get

$$u(x)=-x^2+(17/2)x-(7/2)$$ which is our steady state temperature distribution