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: ODE, seperation of variable

  1. Sep 23, 2010 #1

    fluidistic

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Verify that the following ODE can be reduced to an ODE of separable variables.
    [tex]\frac{dy}{dx} =f(ax+by+c)[/tex] where a, b and c are constants.


    2. The attempt at a solution
    I think I must show that there exist functions g and h such that [tex]g(y)dy=h(x)dx[/tex].
    I have that [tex]dy=f(ax+by+c) dx[/tex]. I was at a loss. So I talked to a friend and he told me to write [tex]u=ax+by+c[/tex].
    So I get [tex]dy=f(u)dx \Rightarrow y= \int f(u)dx=\frac{u-ax-c}{b}[/tex], [tex]y'=\frac{u'-a}{b}[/tex], [tex]y''=u''[/tex]. I want to write [tex]f(u)[/tex] as [tex]\phi _1 (x) \phi _2 (y)[/tex] but I'm totally stuck.
    I'd love a tip.
    Thank you.
     
  2. jcsd
  3. Sep 23, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have figured out that y' = (u'-a)/b and if you plug that in for y' you get

    (u'-a)/b = f(u)

    Write u' as du/dx and, remembering that a and b are constants, see if you can't get the u terms and the x terms on opposite sides.
     
  4. Sep 23, 2010 #3
    ya lckurtz sums it up

    also try looking here:http://www.tutorvista.com/math/separable-differential-equation" [Broken]
     
    Last edited by a moderator: May 4, 2017
  5. Sep 27, 2010 #4

    fluidistic

    User Avatar
    Gold Member

    Thank you guys, I got it.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook