Question

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

Answer 1

what is Yp

Answer 2

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..

Answer 3

woops, Yh = Aexp(2x) + Bxexp(2x)

Answer 4

i m puzzled...........

Answer 5

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)