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: Differential equation

  1. Feb 7, 2007 #1
    Can anyone help me solve

    [tex]\dot{x} = Hx_0 \left( \sqrt{B} \frac{x_0}{x} + \sqrt{1-A-B} \right)[/tex]
     
  2. jcsd
  3. Feb 7, 2007 #2

    mjsd

    User Avatar
    Homework Helper

    what is what? in any case, try integrating factor method
     
  4. Feb 7, 2007 #3
    It's equivalent to solving

    [tex]y \frac{dy}{dx} + ay + b = 0[/tex]
     
  5. Feb 7, 2007 #4

    HallsofIvy

    User Avatar
    Science Advisor

    We need more information. Are you saying that A, B, H, and x0 are constants? Is so, simplify by letting
    [tex]U= \frac{H\sqrt{B}x_0^2}{x}[/tex]
    and
    [tex]V= Hx_0\sqrt{1- A- B}[/itex]

    So your equation becomes
    [tex]\frac{dx}{dt}= \frac{U}{x}+ V= \frac{U+ Vx}{x}[/tex]
    [tex]\frac{xdx}{U+ Vx}= dt[/itex]

    That's easy to integrate.
     
    Last edited by a moderator: Feb 7, 2007
  6. Feb 7, 2007 #5
    Then I get

    [tex]t= \frac{x}{V} -\frac{U}{V^2}ln(Vx+U)[/tex]

    and trying to solve this for x is rather difficult?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...