Let X=(0,∞) x R and y=>g(y) be a given function. Find the solution:

(x,y)==>u(x,y)

To the initial value problem

(-x-y)u_x(x,y)-(y)u_y(x,y)+u(x,y)=0 for all (x,y)belonging to X

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

I keep getting stuck; Any help would be amazing!

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