How to solve p(D)x=f(t) when f(t) is a polynomial of t using operator notation

    –expanding of MIT OCW 18.03 Video Lecture 13

    1.Goal

    My Goal in this paper is showing you, as clearly as I can, how to solve(find a particular solution of) a linear differential equation with constant coefficients: , when f(t) is exp(at), t^n, sin(at) or their sum and multiply.

    For example you can solve equations as fellows, using operator notation, after reading this paper:

    x’+x=t*exp(t)
    x”+x’=t^2
    x”+2x+5x=exp(-2t)cos(t)+4+5t^2
    x”+x’+x=t*exp(t)*sin(t)

    Before your reading of the rest of this paper, I strongly recommend you to watch the 13th video Lecture of Differential Equations on MIT_OCW which can be downloaded on http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring2004/CourseHome/index.htm. The fellowing section is based on that lecture.

    full contents of this paper can be download on
    http://www.freewebs.com/chaosconst/Papers/EX_Lec13.pdf

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