I appreciate it if you can share any thoughts that you may have regarding how to solve the following PDE:
arises due to a boundary condition, but it is unknown and should be derived by solving the PDE itself (details are irrelevant).
A typical strategy would be using Method of Characteristics to tackle this. But can't be dealt with.
Specifically, I am stuck when integrating both sides of the following subsidiary equation due to :
I greatly appreciate it if you could share any thoughts you might have regarding how I can proceed to solve this through this method or any other method.