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Dividing differential equations

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    This is more of a problem I have with my knowledge of differentials. I have two second order differential equations for variables X(a) and T(a). I want to get an expression for X(T). I know I have to divide them, but how do you go about dividing them if they are explicitly stated as:

    eqn1: [tex]\frac{d^{2}X}{da^{2}}[/tex] = Some polynomial


    eqn2: [tex]\frac{d^{2}T}{da^{2}}[/tex] = Some polynomial

    3. The attempt at a solution

    I know for first derivative with respect to 'a', you can just divide them directly and the 'da' part will just cancel, but what would you get for a second derivative?

    Example of first derivative would be:

    dX/da divided by dT/da would equal dX/dT, and you could just solve the resulting simple differential equation to get X(T).
  2. jcsd
  3. Feb 24, 2009 #2
    Ok, maybe I should give the RHS of the equations too..

    eqn1: [tex]\frac{d^{2}X}{da^{2}}[/tex] = -X [tex]\frac{dT}{da}}[/tex] [tex]\frac{dT}{da}}[/tex]

    eqn2: [tex]\frac{d^{2}T}{da^{2}}[/tex] = [tex]\frac{-2}{X^{2}}[/tex] [tex]\frac{dX}{da}}[/tex] [tex]\frac{dT}{da}}[/tex]
  4. Feb 24, 2009 #3
    Never mind, I'm retarded. I just expressed the second order derivative as :

    d/da(dX/da) and when you divide it by d/da(dT/da) the d/da part cancels because its just like an operator. I got an exponential result as X(T) = exp(T/sqrt(2))
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