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Homework Help: Please check my work: verify that the equation is homogeneous

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data
    verify the equation is homogeneous and solve.. thanks

    (x^2 - 2y^2)dx + (xy)dy = 0

    (x^2 - 2y^2) = -(xy)dy/dx

    (x^2 - 2y^2)/-(xy) = dy/dx

    -(x/y) - 2(y/x) = dy/dx



    v = (y/x) .. y = vx and dy/dx = v + xv'




    -(1/v) - 2v = v + xv'

    x(dv/dx) + (1/v) + 3v = 0

    3v + (1/v) = -x(dv/dx)

    (3v + (1/v))/dv = -x/dx

    (1/3v + v)dv = (1/x) dx

    1/9v^3 + 1/2v^2 = ln|x| + c


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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