Will_the_Turtle

$u_t=u_x{}_x+8 ,u(0,t)=-4 ,u(1,t)=4$ since we are looking for a steady state we are looking for when $$u_t=0$$ because our equation should not change with respect to time. By looking at our first equation we integrate up $$u_x{}_x$$ and net $$u=-4x^2+Ax+B$$ with A and B being some constants. We then solve for A and B using our initial conditions and get B=-4 and A=12 so our steady state looks like $$u(x,t)=-4x^2+12x-4$$

The distance of the midpoint from the equilibrium at time t=1.3 is approximately .265