Hi, I just started studying PDE's so sorry for the newbie questions

I have two questions

1. Solve

2. Solve

Here is what I have so far for #1:

Using change of variables

This is where I get stuck. How do i solve for u in this case?

For #2, I'm not sure how to start but I want to say its unsolvable because its inhomogeneous? (probably way wrong in saying that haha)