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Homework Help: Integratable combination question

  1. Jan 17, 2007 #1
    1. The problem statement, all variables and given/known data

    Obtain the general solution of [tex]2xydy - 6y^2dy + 8xdx + y^2dx = 0[/tex]

    2. The attempt at a solution

    [tex]2xydy - 6y^2dy + 8xdx + y^2dx = 0[/tex]

    [tex]2xydy + y^2dx = 6y^2dy - 8xdx[/tex]

    [tex]\intd(xy^2) = \int6y^2dy - 8xdx[/tex]

    [tex]xy^2 = \frac{6y^3}{3} - \frac{8x^2}{2}+C[/tex]

    [tex]xy^2 = 2y^3 - 4x^2+C[/tex]

    3. The problem statement, all variables and given/known data

    Find the particular solution of the DE that satisfies the condition y = 5 when x = 1

    4. The attempt at a solution

    [tex]xy^2 = 2y^3 - 4x^2+C[/tex]

    [tex](5)^2 = 2(5)^3 - 4+C[/tex]

    [tex]25 = 250 - 4+C[/tex]

    [tex]C = -221[/tex]

    Does all of this look right to you? I'm not so sure about the last part?
     
  2. jcsd
  3. Jan 17, 2007 #2
    i think it looks good....but i am always wrong about these things....can someone else see if this is correct or not
     
  4. Jan 17, 2007 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's right. Did you really tex all of that up to get someone to check your arithmetic? :smile:
     
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