Ok, so I've been trying to solve this for a while now and I don't seem to get anywhere. Hope someone can point in the right direction.

We have the PDE

where

are independent variables and

.

So, I know that the equations for the characteristics in this case are

but, I don't see how I can obtain

from here, I've tried playing with the coefficients in the original, isolating

or

but that gets me nowhere. I'm thinking of proposing the curve

as a characteristic, but I haven't checked if it is. So, if someone could give any hints as to how to solve this it would be appreciated.