Method of characteristics

Homework Statement

solve using method of characteristics
$$y \frac{ \partial u}{ \partial x} - x \frac{ \partial u}{ \partial y}= 1$$ where u(x,0) = 0 for 0<x<infinity

The Attempt at a Solution

$$\frac{ \partial y}{ \partial x} = \frac{x}{y}$$ which gives $$y^2+x^2= k$$ the projected characteristic. but its the second part that is giving me trouble when i go to find $$\frac{ \partial u}{ \partial x} = \frac{1}{y}$$ which doesnt work out right...any suggestion anyone?

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tiny-tim
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hi gtfitzpatrick!

(have a curly d: ∂ )

∂y/∂x = x/y gives y2 minus x2 = k

hi gtfitzpatrick!

(have a curly d: ∂ )

∂y/∂x = x/y gives y2 minus x2 = k
my mistake it should have read [/SIZE]

∂y/∂x = -x/y gives y2 + x2 = k

but dont know how to work the second part?

oh and hi back