help with ODE

Discussion in 'Programmer's Corner' started by braddy, May 8, 2006.

  1. braddy

    Thread Starter Well-Known Member

    Dec 29, 2004
    83
    0
    Sorry I made a mistake about the forum. I tried to delete it but I dont see where to do it pleas redirect this post in homework help/math
    Hi ,
    please can I have your help?

    x^2+2 and x^2-2 are fundamental set of solutions of a second order ODE. find the ODE.
    form:y''+p(x) y'+ q(x) y=0.

    I tried to replace the two solutions in the equation but because those solutions have exact same first and second derivatives, I found p(x)=q(x)=0 !!!!

    Can you help me to find p(x) and q(x)?
    Thank you
    B.
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,144
    1,790
    Polynomials are not generally the solutions of ODEs. Generally exponetial functions are required. I'm not familiar with the specific terminology "fundamental set of solutions". I'm familiar with a general solution involving two arbitrary constants in the case of a second order equation and I'm familiar with the particular solution based on the initial conditions. Can you be more precise about the notion of fundamental set of solutions?

    Here is my next problem. If y is a function of x, then the expression above is not a differential equation at all but a simple product of polynomials, which should have an algebraic solution. This solution may not be unique since p(x) and q(x) do not appear to be constrained.
     
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