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Undetermined coefficient method

  1. Oct 17, 2015 #1
    1. The problem statement, all variables and given/known data
    y''+10y'+25y=x+2+3e-5*x

    2. Relevant equations


    3. The attempt at a solution
    F(D) = D2+10D+25 zeroes: -5
    yc= C1*e-5*x + C2*e-5*x *x

    yp = ax+b + C*e-5*x
    yp = ax+b + C*e-5*x*x2

    I just want to know if my yc and yp is correct, after that I know how to do it.
     
  2. jcsd
  3. Oct 17, 2015 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    yc is correct, yp is not. The SECOND yp, [itex]ax+ b+ cx^2e^{-5x}[/itex] is correct. Since [itex]e^{-5x}[/itex] and [itex]xe^{-5x}[/itex] satisfy the associated homogenous equation you need the "[itex]x^2[/itex]".
     
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