First order linear PDE,but tricky. Need help

[ProphetX]

Hello everyone! A first order linear PDE appears in a model I describe, but I can't get the right solution by hand/computing it. Wolfram gives it, but if I try with the characteristic equation method,I can't get there. can someone help? Gamma and mu are constants.

 

[ProphetX]

I wrote the characteristics as follows,but if I let wolfram solve them or I solve them by hand, and combine them into the final solution, I don't get the right answer,which wolfram provides.Any clues where I could be mistaken?