I would be incrediabely gratful if someone could go through step by step and explain how to do this question, as i'm rather stuck -and the lecture notes have a lot to be desired!
'Find $z(x,y)$ explicitly if
and $z(x,0)=1$ for $x \geq 1$
So i'm trying to go about solving the characteristics of this, the equations
Then use the solution along the curve $l(t)=(t,0,1)$ for $t\geq 1$ to find the coefficients of the solutions to the equation in terms of t. We would then have the solution space in terms of parameters $t,s$ correct? Then we try to eliminate these to get the space in terms of $x,y,z$. I can't seem to solve the equations however.
Any help is greatly appreciated.