1. Limited time only! Sign up for a free 30min personal 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!

Diff. Eq. Show that the following equation is not exact.

  1. Mar 2, 2014 #1
    1. The problem statement, all variables and given/known data

    Show that the following equation is not exact.
    Then find and simplify the integrating factor that makes the equation exact.(You do not have to solve the equation)

    (Y^2 - x)dx + (4xy)dy=0

    2. Relevant equations



    3. The attempt at a solution

    M(x,y) =(Y^2 - x)dx N(x,y)=(4xy)dy

    Partial Derivative of m with respect to y is 2y

    Partial Derivative of N with respect to x is xy

    ^shows they are not exact.
    how exactly do i find this integrating factor that makes them exact?
     
  2. jcsd
  3. Mar 2, 2014 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If your text doesn't tell you how, look here:

    http://www.cliffsnotes.com/math/differential-equations/first-order-equations/integrating-factors
     
  4. Mar 2, 2014 #3
    yes!!! thank you so much. I figured it out with the link you gave me.
    My integrating factor was x^-(1/2) yay :)
    they are exact now.

    I found it really strange my book does not show me how to find the IF for exact equations, and the homework examples already have the IF given. hmmm. anyways.

    can you answer another question for me. In the link I used case 1. but i am unsure when i need to use case2. the conditions are nearly identical.

    Consider the differential equation M dx + N dy = 0. If this equation is not exact, then M y will not equal N x ; that is, M y – N x ≠ 0. However, if

    case1 is a function of x only
    (My-Nx)/(N)

    Case2 is a function of y only
    (My-Nx)/(-M)
     
    Last edited: Mar 2, 2014
  5. Mar 3, 2014 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If the equation is exact so ##M_y=N_x##, you don't need an integrating factor. It's ready to go as it is.

    You don't have a choice of which, if any, case to use. If you are lucky and get either the function of x or function of y in that test, you can find an integrating factor which will make the equation exact. But an equation might not be exact and neither of the above cases work either. Then you have to resort to other methods to solve it, presuming it can be solved analytically at all. These techniques don't always work.
     
  6. Mar 3, 2014 #5

    thank you for explaining this to me :) It all makes sense to me now!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Diff. Eq. Show that the following equation is not exact.
Loading...