Or as I used to call them, Particularly Difficult Equations.

You see, the trick to a PDE is to use the LOFL transform. The LOFL transform (Leap Of Fuggin Logic) moves your PDE into easy space. Easy space has the important property that all problems are trivial and or linear. Once you've solved you're PDE in easy space you just apply the inverse LOFL and you're done.

How do you take a LOFL transform you ask? That's left as an exercise for the reader.