Problem: Given the following PDE:$$\frac{\partial y}{\partial t} = \frac{\partial^2y}{\partial x^2} - y^5, \quad y(x,t)>0$$For the $D\frac{\partial^2y}{\partial x^2}$ and $ \alpha y^5 t$ terms of the same order of magnitude, find the asymptotic behavior of $y$ at times after $y$ blows up. Please place your final solution in a $\boxed{}$ LaTeX Environment. Don't use a * symbol in your notation.
Solution: $\boxed{y(x,t) = (3/4)^{1/4} x^{-\frac{1}{2}}}$