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Problem solving 2nd order ODE not for the faint of heart

  1. Apr 9, 2008 #1
    Problem solving 2nd order ODE...not for the faint of heart!!

    Hey folks,

    I'm having problems solving the following set of ODE's:

    [tex]3H_a^2+H_b^2+6H_aH_b=k_1\rho[/tex] eq.1

    [tex]\dot{H_a}+3H_a^2+2H_aH_b=k_2\rho[/tex] eq.2

    [tex]\dot{H_b}+2H_b^2+3H_aH_b=k_3\rho[/tex] eq.3

    These are cosmological equations. Note, [itex]\rho=\frac{1}{b^6}(1-b^2+b^4)[/itex], also the H's are Hubbles constant in a and b, eg



    The a's and b's are functions of t (time) and the k's on the RHS are just constants. I want to put this all together and ultimately plot a as a function of t and b as a function of t.

    The equations originate from the paper: http://arxiv.org/abs/0707.1062 , equations 9,10,11 and I am trying to duplicate the plots in fig1.

    What I'm thinking:

    Solve eqtn 1 for [itex]H_a[H_a] using the quadratic eqtn then plug that into 3 and use DSOLVE in mathematica.

    Can anyone let me know if this is the correct approach.

    Thanks in advance!!

    Last edited: Apr 9, 2008
  2. jcsd
  3. Apr 9, 2008 #2
    Actually I tried the above

    and mathematica tells me Solve::svars: Equations may not give solutions for all "solve" variables
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