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A simple(!) ODE

  1. Jan 11, 2010 #1
    1. The problem statement, all variables and given/known data

    How can you solve an arrogant ODE of form [tex]{\frac {\left( {\frac {d}{dt}}\rho \left( t \right) \right) ^{2}}{\rho \left( t \right) }}=-3[/tex]??

    3. The attempt at a solution

    I don't have any idea... maybe you do!

    Thanks
    AB
     
  2. jcsd
  3. Jan 11, 2010 #2

    Mark44

    Staff: Mentor

    From this you get [itex](\rho '(t))^2 = -3\rho(t)[/itex] from which you get two equations

    [tex]\rho '(t) = +\sqrt{-3\rho(t)}[/tex]

    and

    [tex]\rho '(t) = -\sqrt{-3\rho(t)}[/tex]

    Both are separable.
     
  4. Jan 11, 2010 #3
    Sorry. I'm a little bit confused right now, but how would this separation help us to get [tex]\rho(t) [/tex]?

    AB
     
  5. Jan 11, 2010 #4
    If you divide both sides by sqrt(rho), you get:

    rho'/sqrt(rho) = +/-sqrt(3) i

    You can write this as:

    d rho/sqrt(rho) = +/-sqrt(3) i dt

    You can now integrate both sides.
     
  6. Jan 11, 2010 #5

    zcd

    User Avatar

    a simple ODE with a complex answer :D
     
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