If u = ln (x^2 + y^2)/(x + y), find the constant k such that x dy/dx + y du/dy = k

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asked by phiri
  1. well, just plug and chug:

    u = ln(x^2+y^2) - ln(x+y)
    ∂u/∂x = 2x/(x^2+y^2) - 1/(x+y)
    ∂u/∂y = 2y/(x^2+y^2) - 1/(x+y)

    x ∂u/∂x + y ∂u/∂y = 2x^2/(x^2+y^2) - x/(x+y) + 2y^2/(x^2+y^2) - y/(x+y)

    = 2(x^2+y^2)/(x^2+y^2) - (x+y)/(x+y)
    = 3

    so, k=3

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    posted by Steve

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