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Math Help - How does one show this using characteristics?

  1. #1
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    How does one show this using characteristics?

    If U = U(x,y,z) satisfies

    (y-z)dU/dx + (z-x)dU/dy + (x-y)dU/dz = 0,

    then show that U contains x, y and z only in the combinations x+y+z and x^2+y^2+z^2. In other words U = f(x+y+z, x^2+y^2+z^2).
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