I am working to solve a PDE with the given initial condition $$u(x_0,y)=y$$ where $x_0$ is a constant. In order to solve the PDE I need to parameterise the curve in the form $\Gamma(s)$. I have parameterised it so far... $$u=s,\ y=y,\ x=x_0$$ I'm not entirely sure if it right as when I use this parameterisation the solution to the PDE isn't right (albeit pretty close).
Please may someone help me parameterise this curve. Many thanks in advance.