Question: Urgent: So I have this PDE

I  have to solve this initial value problem:

pde := (-x+y)*(diff(u(x, y), x))+(-y*(diff(u(x, y), y)))+c*u(x, y)=0

subject to u(0,y)=g(y)

I have had a go and this is what I have so far:

a := -x(s)+y(s)

b := -y(s)

c := 1

pde := a*(diff(u(x, y), x))+b*(diff(u(x, y), y))+c*u(x, y) = 0

chareq1 := diff(x(s), s) = a

chareq2 := diff(y(s), s) = b

ic1 := x(0) = 0

ic2 := y(0) = y[0]

charcurve2 := dsolve({ic2, chareq2})

charcurve1 := dsolve({ic1, chareq1})

How do I finish this off?!?!?! Any help would be appreciated :)

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