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Homework Help: Find the general solution of the following differential equation

  1. Aug 26, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the general solution of the following differential equation:
    x.(dy/dx) = y + sqrt.[(x^2) - (y^2)]

    2. Relevant equations
    I'm working through my excerise book and have been able to get through quite a few differential equations with success, but this one really does stump me. I think it's the sqrt.[(x^2) - (y^2)] that gets me confused.

    3. The attempt at a solution
    My first step was to divide both sides by x to get dy/dx alone, hence:
    (dy/dx) = y + [ sqrt.[(x^2) - (y^2)] / x ]

    This is where I begin to get lost. My natural instinct is to try and separate the x and y's but I can't seem to and the next step for is a mystery to me. I'm having a lot of troule identifying what sort of approach to use.

    Any help would be very appreciated, thank you in advance.
  2. jcsd
  3. Aug 26, 2007 #2


    User Avatar
    Homework Helper
    Gold Member

    Not quite. You get,

    (dy/dx) = y/x + sqrt.[1 - (y/x)^2]

    Try y=ux
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