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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

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    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

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    Staff Emeritus
    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?
     
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