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## Homework Statement

solve x

^{2}u

_{x}+ y

^{2}u

_{y}= 0 for u(2,y) = y

## Homework Equations

## The Attempt at a Solution

with a = x

^{2}and b = y

^{2}

y' = b/a = (y/x)

^{2}this can be solved for y by separation of variables:

[itex]y = \frac{x}{1-xC}[/itex]

and

[itex]C = \frac{y-x}{xy}[/itex]

now

[itex]u(x,y) = f(C) = f(\frac{y-x}{xy})[/itex]

applying initial value conditions

[itex]u(2,y) = f(\frac{y-2}{2y})[/itex]

this is where my understanding runs out. how do i determine f according to the initial value? i have looked at several books but they just assume this step is obvious

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