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Special Integrating Factors

  1. Apr 27, 2015 #1
    1. solve the problem first finding an integrating factor of susceptible form.
    y(x+y)dx+(xy+1)dy=0



    2. Relevant equations
    form: M(x,y)dx+N(x,y)dy=0
    intigrating factor: eint(1/n(dm/dy-dndx)dx

    3. The attempt at a solution
    u(x)=eint(1/(xy+1)(y(x+y)d/dy-(xy+1)d/dx)dx
    this reduces to
    eint((x+y)/(xy+1))dx

    This is where I need help. my integration is not good. I know that if I can solve for the integrating factor then I can solve for the equation because it will be in exact form.

    Thanks for any help.
     
  2. jcsd
  3. Apr 28, 2015 #2

    HallsofIvy

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    This makes no sense to me. Your integrand is a function of x and y but you are integrating with respect to x so the exponent will be a function of y only yet you say that equals a function of x!

     
  4. Apr 28, 2015 #3
    edited to make it easier to read
     
  5. Apr 28, 2015 #4
    Halsofivy, you are right u(x) should be in terms of x. the way it works out in the book examples is y gets factored out while solving for the intigal. leaving only a function of x.
     
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