This is my third question regarding PDE solvable as ODE and I am still confused because the book I am following (Advanced Engineering Mathematics by Erwin Kreyszig) has only two very elementary examples where as I find the exercise problems to be very difficult, especially in their approach.

Currently I am having problem in Q5 of Problem Set 12.1.

How do I approach this one. I write

in differential form but then I do not know how to handle the

part. Can someone please explain the solutiion to this one.

And please can I be provided with some links to online examples for PDEs solvable as ODEs ?