General Solution for the characteristics of 2 quasi linear PDE's

Hi all,

I am stuck on how the general solutions where obtained for the following quasi linear PDE's. I understand this to be quasi linear because the highest derivative of u is linear even though e^u is nonlinear.

Anyway,

1) and 2)

I calculate the characteristics of 1) and 2) as

1)

hence however I dont know how this arrived at

How are there 2 constants a and b when it is only a first order ODE?

2)

hence which arrives at

I dont know how x,y and t+c are determined?

Any tips will be appreciated.

Thanks

bugatti79