Problem: solve$ \partial_t u = (u^3-2(x-2t)) \partial_x u - \partial_x \left( u \partial_x u \right) - (x-2t)^{-3} $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: $\boxed{u(x,t)=-\frac{1}{254 (x-2t)^2}-\frac{2}{16129 (x-2t)}+\frac{4 \log (x-2t)}{2048383}-\frac{4 \log (127-2 (x-2t))}{2048383}+5}$