1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating factor

  1. Jan 31, 2006 #1
    Hey everyone,
    I need to find an integrating factor of the form x^n*y^m, to solve a differential equation i have... however i do not know the process to solve for an integration of this form.. .any help??
    Thanks
    Steph
     
  2. jcsd
  3. Jan 31, 2006 #2
    can you give an example problem that your working on?
     
  4. Jan 31, 2006 #3
    the problem is ( 12 + 5xy )dx + (6 (x/y)+ 3x^2)dy =0
    and it says, find an integrating factor of the form (x^n) * (y^m), and solve the equation...
    thanks sweetie
    steph
     
  5. Feb 1, 2006 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    RULE 1: Mathematics problems are not solved by staring at a problem until you remember the answer! They are solved by plugging things in and doing the algebra.
    So TRY!!

    If you multiply the equation by [itex]x^ny^m[/itex] you get
    [itex](12x^ny^m+ 5x^{n+1}y^{m+1})dx+ (6x^{n+1}y^{m-1}+ 3x^{n+2}y^m)dy= 0[/itex]

    In order for that to be an exact equation, you must have
    [itex](12x^ny^m+ 5x^{n+1}y^{m+1})_y= (6x^{n+1}y^{m-1}+ 3x^{n+2}y^m)_x[/itex]

    Do the derivatives and see what m and n must be for those to be equal!

    [itex](12x^ny^m+ 5x^{n+1}y^{m+1})_y= 12mx^ny^{m-1}+ 5(m+1)x^{n+1}y^m[/itex]
    [itex](6x^{n+1}y^{m-1}+ 3x^{n+2}y^m)_x= 6(n+1)x^ny^{m-1}+3(n+2)x^{n+1}y^m[/itex]
    Coefficients of the same powers must be equal. That gives two equations for m and n.
     
    Last edited: Feb 1, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Integrating factor
  1. Integrating factor (Replies: 12)

  2. Integrating factors (Replies: 6)

  3. Factoring an Integral (Replies: 8)

  4. Integrating Factor (Replies: 4)

  5. Integrating factor (Replies: 5)

Loading...