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Math Help - Second Order inhomogeneous O.D.E: Particular Integral when f(x)=x^k (k<0)

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    Second Order inhomogeneous O.D.E: Particular Integral when f(x)=x^k (k<0)

    Hey guys,

    What form of approximations of particular integral do I choose when the forcing f(x) is a polynomial of a negative order?

    Here is my O.D.E which I'm solving:



    I've made a Euler variable substitution of t=lnx which has removed the non-constant coefficients. This gives:

     \ddot{y}+3\dot{y}+2y=\frac{3}{t^{2}}

    Normally for a polynomial of degree n where n>0, I'd just try a generic polynomial of degree n with all terms down to the integer.

    Any ideas folks?

    Edit: Stupid mistake with the variable substitution. Nothing to see here!
    Last edited by nugiboy; December 8th 2013 at 02:36 PM.
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