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Differential Equation Challenge

  1. Oct 28, 2011 #1
    Solve showing full working
    (x^2 -1)y' + 2xy = x

    You must show full working.
     
  2. jcsd
  3. Oct 28, 2011 #2

    lurflurf

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    Homework Helper

    No full workings here, were fresh out.
    Try to rearrange and find an integrating factor u such that
    u(x^2 -1)y' + u(2xy - x)

    is and exact differential
     
  4. Oct 28, 2011 #3
    Find the integerating factor "u"
    So I have to rewrite the equation in the standard form y' + Py =Q
    IF = e ^ ∫P.dx
    where P = 2x ???
     
  5. Oct 28, 2011 #4
    Thanks....I solved it my solution is
    y(x^2 -1)=(x^2)/2
     
  6. Oct 28, 2011 #5

    lurflurf

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    Good, but you need the arbitrary constant
    y(x^2 -1)=(x^2)/2+C
     
  7. Oct 28, 2011 #6
    I must commend you guys for all the assistance and I will surely recommend you guys to my friends. Thanks again.
     
  8. Nov 2, 2011 #7

    CGZ

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    (x^2 - 1 ) y' + 2xy = ((x^2-1)y)' = x;-->
    (x^2-1)y = \int{x};-->
    (x^2-1)y = 0.5 x^2 + C

    y = (0.5 x^2 + C) / ( x^2 - 1 )
     
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