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!

Homework Help: Another O.D.E

  1. Oct 17, 2005 #1
    for the following question:

    my problem:
    so (1/F)(dF/dx)=2
    so e^2x-(e^2x)(6e^y-2x)dy=0
    so (integration)(d^2x)dx=(1/2)e^2x +h(y)
    =>h(y)= -6e^(2x+y)+xye^2x+c
    so (1/2)e^2x-6e^(2x+y)+xye^2x+c-0

    however the correct answer should be

    does anybody know where my calculations went wrong?
  2. jcsd
  3. Oct 17, 2005 #2


    User Avatar
    Homework Helper

    Your correct answer hasn't got an x-term in it. Is that a typo ?
  4. Oct 18, 2005 #3
    no, it's not a typo~
  5. Oct 19, 2005 #4


    User Avatar
    Homework Helper

    Did a little research on this. Finally figured out what you were trying to do
    You have a differential equation and you were trying to force it to be an exact DE, yes ?

    I'm afraid you got the integrating factor wrong.
    You had,

    (1/F)dF/dx = 2,

    that should have been

    (1/F(y))dF(y)/dy = 2


    F(y) = e^(3y)

    Also, your "correct answer" is wrong,

    [tex]y = ce^{-2y} + 2e^y[/tex]

    There is no x-term in this eqn, so you have no relation between x and y, so you can't use this eqn to get a DE that involves an x, since x was never involved in the first place.

    The actual answer is,

    [tex]c = x.e^{2y} - 2e^{3y}[/tex]
    [tex]x = c.e^{-2y} + 2e^y[/tex]

    If you differentiate that, you'll end with the DE you started with.
    Last edited: Oct 19, 2005
  6. Oct 19, 2005 #5


    User Avatar
    Science Advisor
    Homework Helper

    HINT:Make [itex] e^{y(x)}=t(x) [/itex]

  7. Oct 19, 2005 #6
    opps... i corrected the integrating factor and it works! f=e^2y~
    why did you think of making [itex] e^{y(x)}=t(x) [/itex]?
  8. Oct 19, 2005 #7


    User Avatar
    Homework Helper

    I guess that's a substitution you get to know with experience ?

    It's faster/simpler than doing the exact differential thing.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook