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Differential Equations - Auxiliary Equation Method - Few Questions watch

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    1) For the following D.E:

    \frac{d^2y}{dx^2}+6\frac{dy}{dx}  +10y=3sint

    Now, I've got the Complimentary Function, in the form of:

    y=e^{-3t}(Asint+Bcost)

    Therefore, for the trial function of my Particular Integral, do I use:

    y=ltsint+mtcost

    or

    y=ltsint+mcost


    Whichever I do use, when I differentiate my trial function (both times) and substitute my derivatives back into my original D.E, I tend to get two simultaneous equations but both in terms of m, l and t. Should I still have t in my equation? If so, do I try to eliminate it somehow, or keep my constants in terms of t?

    2) Next D.E:

    \frac{d^2y}{dx^2}+3\frac{dy}{dx}  +2y=3x^2

    What would be my Particular Integral for this equation? Simply cx^2 where c is a constant? It just I've never came across this kind of linear equation before and am not sure on what the trial function should be.


    Thanks for any help, much appreciated.
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    X is always equal to 17. They don't want you to know that.
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    (Original post by bawlmorian)
    X is always equal to 17. They don't want you to know that.
    Ahhhhhhh I see it now.

    All this time. I now know where I'm going wrong.

    Oh wai-
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    2) you need to guess a P.I of the form ax^2 + bx + c (ie if you're given a polynomial of degree n look for a forcing term of degree n).
 
 
 
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