Results 1 to 3 of 3

Math Help - Ordinary Differential equation

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    12

    Ordinary Differential equation

    A uniform chain of total length 8 metres, settle 1 metre above the ledge and 2 metres hang on the other side. If x represents the length. The motion of the chain is

    (x+1)v(dv/dx) + v^2 = (x-1)g

    where v is velocity and g is a gravitational constant
    show that by making the substitution u = v^2 we obtain
    {du}/{dx} + (^{2}/_{x+1})u=2(^{x-1}/_{x+2})g

    now do i have to integrate this in order to subsitute?
    any help on this would be appreciated as i have no idea where to start cheers people!.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Why not use an integrating factor?

     \phi (x) = e^{\int p(x)dx}

     \phi (x) u(x) = \int \phi (x) r(x) dx

    Where

     \frac{du}{dx} + p(x)u = r(x)

    Is the format.

    Sorry, the above is what you would do to solve after substitution. You don't need to integrate BEFORE you substitute.

    I'm fairly sure your of the latter equation should be  2 (\frac{x-1}{x+1})g , no?

    If that's the case:

    Divide through by  x+1

    After that apply the following considerations:

     u = v^2

     \frac{du}{dv} = 2v

     vdv = \frac{1}{2}du

     \frac{dv}{dx}v = \frac{1}{2}\frac{du}{dx}

    Should help!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2007
    Posts
    12

    thanks

    brilliant cheers got it!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ordinary Differential Equation Help
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: February 19th 2011, 12:29 PM
  2. ordinary differential equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 7th 2010, 09:08 AM
  3. First order ordinary differential equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 13th 2010, 02:46 PM
  4. Ordinary Differential Equation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 23rd 2007, 10:24 AM
  5. Ordinary Differential Equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2007, 07:20 PM

Search Tags


/mathhelpforum @mathhelpforum