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Differential Equation first order help

  1. Jul 18, 2006 #1
    Can anybody tell me what can be the solution of this differential equation?

    (dr/dt)^2=a/r^2+b/r+c
    Is first order and i need some ideas about solving it
     
  2. jcsd
  3. Jul 18, 2006 #2

    StatusX

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    What have you tried? I'd suggest starting by multiplying both sides by dr/dt, and trying to get each side into the form d/dt(something).
     
  4. Jul 18, 2006 #3

    arildno

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    This is a separable diff.eq. You may rewrite it as:
    [tex]\frac{rdr}{\sqrt{a+br+cr^{2}}}=\pm{dt}[/tex]
    This can be readily integrated, yielding an implicit equation for the function r(t).
     
  5. Jul 18, 2006 #4
    you are right,
    the answer was obvious.i guess i need to rest a little. thank you guys.
     
    Last edited: Jul 18, 2006
  6. Jul 18, 2006 #5

    arildno

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    As a hint, you ought to rewrite the left-hand side as:
    [tex]\frac{rdr}{\sqrt{cr^{2}+br+a}}=\frac{dr}{2c}(\frac{2cr+b}{\sqrt{cr^{2}+br+a}}-\frac{b}{\sqrt{cr^{2}+br+a}})[/tex]
     
  7. Jul 18, 2006 #6

    StatusX

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    Sorry, I thought that was d^2/dt^2.
     
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