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Homework Help: Intergrating factor

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data

    (2y-6x)dx + (3x+4x2y-1)dy = 0

    2. Relevant equations



    3. The attempt at a solution

    (3xy+4x2)dy/dx = 6xy-2y2


    i'm stuck, want to find the intergrating factor, it's xy2 when i reverse from the answer :D.. give me any hint please
     
  2. jcsd
  3. Feb 1, 2010 #2
    or am i suppose to use special integrating factor??
     
  4. Feb 1, 2010 #3

    Dick

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    Are you sure there is an integrating factor? Maybe I'm just not seeing it. But you could also try the substitution v=y/x. That should make it separable.
     
  5. Feb 2, 2010 #4
    yey, i got it now, there's another technique which i don't really know the details..

    But to find suitable intergrating factor,

    its something like


    e([tex]1/M[/tex])[([tex]N(x,y)/dx[/tex]) - ([tex]M(x,y)/dy[/tex])]

    and is equal to xy2

    and multiply both sides by the integrating factor, and will get Exact form of equation and solve it, hoho,

    but maybe i need to try substituting v=y/x
     
  6. Feb 2, 2010 #5

    HallsofIvy

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    Every first order differential equation has an integrating factor- it just may be hard to find!

    Are you required to find an integrating factor? this equation is "homogeneous". Write it as
    [tex]\frac{dy}{dx}= \frac{6x- 2uy}{3x+ 4x^2y^{-1}}= \frac{6- 2\frac{y}{x}}{3+ 4\frac{x}{y}}[/tex]

    Let u= y/x so that y= xu and dy/dx= u+ x du/dx and that will become a separable equation for u as a function of x. If you really want to find an integrating factor, I think that solving for u and then y and deriving the integrating factor from the solution is simplest.
     
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