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Differential Equation/Intial Value Problem

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve the following initial value problem,

    y' = (x-y)/(x+y), y(1) = 1

    2. Relevant equations


    3. The attempt at a solution

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

    dy/dx * (x+y) = x-y

    (x+y)dy = (x-y)dx

    ∫(x+y)dy = ∫(x-y)dx

    xy + y^(2)/2 = x^(2)/2 - xy + C

    2xy + y^2 = x^2 - 2xy + C

    y^2 + 4xy - x^2 = C

    Sub in x=1, y=1

    1 + 4 - 1 = C = 4

    Soln: 2xy + y^2 = x^2 - 2xy + 4
     
  2. jcsd
  3. Jan 25, 2009 #2
    N/m, I just realized this is a homogeneous diffeq. Sorry.
     
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