Intergrating factor

  • Thread starter annoymage
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  • #1
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Homework Statement



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

Homework Equations





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
 

Answers and Replies

  • #2
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or am i suppose to use special integrating factor??
 
  • #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.
 
  • #4
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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
 
  • #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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