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## Homework Statement

solve using method of characteristics

[tex]

y \frac{ \partial u}{ \partial x} - x \frac{ \partial u}{ \partial y}= 1

[/tex] where u(x,0) = 0 for 0<x<infinity

## The Attempt at a Solution

[tex]

\frac{ \partial y}{ \partial x} = \frac{x}{y}

[/tex] which gives [tex]y^2+x^2= k [/tex] the projected characteristic. but its the second part that is giving me trouble when i go to find [tex]

\frac{ \partial u}{ \partial x} = \frac{1}{y}

[/tex] which doesnt work out right...any suggestion anyone?