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Integration Factors

  1. Aug 2, 2008 #1
    I am having issues finding the integration factor for the following two problems. I believe the second one can be solved by inspection.

    1. (y^3+2ye^x)dx + (e^x+3y^2)dy = 0

    2. (x-x^2-y^2)dx + (y+x^2+y^2)dy = 0
  2. jcsd
  3. Aug 3, 2008 #2


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    For the first one, try assuming in turn that the integrating factor is a function of either x or y only, then see if you can come up with it by solving a DE.

    What do you mean by 2nd one being solvable by inspection?
  4. Aug 3, 2008 #3
    I tried using the method described by the book. Setting M= y^3+2ye^x and N = (e^x+3y^2)... then taking dM/dy and dN/dx... then (dM/dy - dN/dx) / N and (dN/dx - dM/dy) / M... I don't know if my problem is that I did something wrong in the derivations but neither gives me an integration factor that is a function of just y or just x.

    As far as the second goes, I meant that the equation needs to be modified so that the above is possible (dM/dy = dN/dx), but I can't figure out how to modify the equation around so that is possible.

    The solutions are supposed to be:
    1. y^3e^x+ye^(2x)=c
    2. ln(x^2 + y^2) +2y - 2x = c
  5. Aug 3, 2008 #4
    never mind. I got it.
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