Problem: solve$ \partial_t u = u^2 \partial_x u - \partial_x \left( u \partial_x u \right) - (x-2t)^{-3/2} $as $t\to\infty, u(\pm infty,t)\to 5$ away from any divergences to a nonconstant function. Place one final solution in a $\boxed{}$ LaTeX Environment
Solution: $\boxed{u(x,t)=-2(x-2t)^{-1/2}/(2+5^3)+5}$