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EXACT equation

  1. Aug 2, 2009 #1

    @m@

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    EXACT equation !!

    hi!! to all
    I want little help about exact equation..
    that the given equation is
    >> ay dx + bx dy= 0
    I had solved and found integrating factor of all of my equations by formula
    P(x) = My-Nx/N
    but for this equation I have got IF for this equation is x((a-b)/b) and after multiplying this factor by equation I cant get exact equation once again :mad:
    and in book answers IF for this equation is x^a-1.y^b-1
    So., can any one tell me how can I solve this eq by method of inspection >>
    plzzz help me!!
     
  2. jcsd
  3. Aug 2, 2009 #2
    Re: EXACT equation !!

    Why not just divide by xy?
     
  4. Aug 2, 2009 #3
    Re: EXACT equation !!

    In order to determine what the integrating factor is you must first normalize the equation.
    [tex]\frac{dy}{dx}+P(x)y=f(x)[/tex]
    is an example of a normalized differential equation, the IF being
    [tex]e^{\int P(x)dx}[/tex].

    Does this help?
     
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