anonymous
  • anonymous
i have a non-homogeneous equation.. And I need to take a guess for Yp. The r(x) = x*exp(3x), i'm not sure what guess for Yp to take
Mathematics
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anonymous
  • anonymous
i have a non-homogeneous equation.. And I need to take a guess for Yp. The r(x) = x*exp(3x), i'm not sure what guess for Yp to take
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
what is Yp
anonymous
  • anonymous
http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx If you look at example one, a guess for Yp is taken based on thier example The actual equation for me is y'' -4y' + 4y = xexp(3x) So far I have Yh = Aexp(2x) + Bexp(2x) Now I need to find Yp..
anonymous
  • anonymous
woops, Yh = Aexp(2x) + Bxexp(2x)

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anonymous
  • anonymous
i m puzzled...........
anonymous
  • anonymous
let yp=xe^3x(ax+b) now differentiating y''=e^3x(9ax+9b+6a) y'=e^3x(3ax+3b+a) and putting the values in y''-4y'+4y=xe^3x you get e^3x((9ax+9b+6a)-(12ax+12b+4a)+(4ax+4b))=xe^3x ax+b+2a=x so a=1, b+2a=0 => b=-2 yp=e^3x(x-2)

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