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Solving ODE with variable coefficients

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data

    I wanted to solve a ode which has Brownian motion as a variable coefficient

    2. Relevant equations

    2x2y'' + y' -ρy = 0

    where x is the Brownian motion with respect to time
    ρ is a constant
    3. The attempt at a solution

    I have tried power series with no solution. Is there a solution to this. IS there any easy way to solve this ODE. Once this ode is tranformed I need to find the roots.
     
    Last edited: Mar 8, 2012
  2. jcsd
  3. Mar 8, 2012 #2
    Any hints

    I have tried to reduce the order but could not.

    Is there any transformation that I can apply. I tried y = xr it did not work

    Please guide me....
     
  4. Mar 8, 2012 #3

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    Maple 13 gives a solution involving exponentials, first degree polynomials, and
    Bessel functions multiplied together. This is also a special case of equation 17 at this link:
    http://eqworld.ipmnet.ru/en/solutions/ode/ode-toc2.htm

    Whether or not that will be helpful to you, I don't know.
     
  5. Mar 10, 2012 #4
    Thanks for the hints.

    I saw the solution in maple15 which involves intergal and exponetials.Its little complex.
    There is a tranformation required for this equation which I'm not able to get

    Also it is not a special case of 17

    Now in short
    I need to know a transformation when you differentiate you get 1 and if you differentiate it again you get x^2
     
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