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Homework Help: Stuck on equating co-efficents! DiffEQ

  1. Feb 24, 2006 #1
    I'm confused on how to equate coniffecents. What i'm doing is, finding a particular solution for just the polynomial then i'm going to find it just for the exponential and add them together rather then putting it all together and making it a mess, but i'm stuck when i try to add the Co-efficents, can someone explain that process to me? Thanks!

    Here is my work!
    http://suprfile.com/src/1/1ta5k1/lastscan.jpg [Broken]
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Feb 24, 2006 #2

    quasar987

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    I kinda see.

    Fact: Two polynomials are equal iff their respective coefficients are the same. (You might want to try proving this (hint set x=0. u get 1 relation, differentiate, set x=0, u get a second equality, differentiate, set x=0, etc))

    This is what you have here. So you want to rewrite the LHS as

    [tex]-At^2 + (2A-B)t + (12A+B-C) = t^2 + t[/tex]

    Now what the theorem/fact stated above is telling you is that

    -A=1
    2A-B=1
    12A+B-C=0

    It's a linear system of equation. Start row-reducin' friend!
     
  4. Feb 24, 2006 #3
    THanks man worked great!!
     
  5. Feb 25, 2006 #4

    benorin

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    There is another method: just plug-in three different values of t (like, say t=0,1,2,) into the given equation to generate three equations in A,B, and C.
     
  6. Feb 25, 2006 #5
    shweet.
    thanks for the tip
     
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