As I continue working through lecture notes for my DE course, I encounter the following as an exercise:
Looking at the PDE
$e^{2y}u_{xx}+u_y=u_{yy}$
how can we find the differential equation satisfied by its characteristic curves and show that $\lambda =x+e^y \text{ and } \mu =x-e^y $are canonical variables for the PDE?
Any help would be very appreciate. Best regards, MM