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I am trying to solve...

u*u_{x}+ u_{y}-u = 0 with i.c. u(x,0) = x +10

Determine: a.) characteristic equation

b.) compatibility equation

c.) value at u(5,10)

I've tried the general method of determining the characteristic equation dy/dx=b/a and attempted a parametrization but I don't think I am coming-up with the correct answer. I keep getting Us or Xs in the result - I am assuming there is a clean answer but I could be wrong.

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# General Method of Characteristics Problem

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