# Undetermined Coefficients

• March 6th 2011, 11:49 AM
JJ007
Undetermined Coefficients
Set up the correct linear combination of functions with undetermined literal coefficients to use in finding a particular integral by the method of UC. (Do not actually find the particular integrals.)

$y''-6y'+8y = x^3+x+e^{-2x}$

$m^2-6m+8=0$

$y_c=C_1e^{2x}+C_2e^{4x}$

$S_1=(x^3,x^2,x,1)$
$S_2=(x,1)$
$S_3=(e^{-2x})$

S_2 is completely contained in S_1 but none are included in the complimentary function?

Thanks.
• March 6th 2011, 12:39 PM
TheEmptySet
Quote:

Originally Posted by JJ007
Set up the correct linear combination of functions with undetermined literal coefficients to use in finding a particular integral by the method of UC. (Do not actually find the particular integrals.)

$y''+6y'+8y = x^3+x+e^{-2x}$

$m^2-6m+8=0$

$y_c=C_1e^{2x}+C_2e^{4x}$

$S_1=(x^3,x^2,x,1)$
$S_2=(x,1)$
$S_3=(e^{-2x})$

S_2 is completely contained in S_1 but none are included in the complimentary function?

Thanks.

$m^2+6m+8=(m+2)(m+4)$
• March 6th 2011, 12:58 PM
JJ007
Quote:

Originally Posted by TheEmptySet
$m^2+6m+8=(m+2)(m+4)$
$y=Ax^3+Bx^2+Cx+D+Me^{-2x}$