# Thread: Undetermined Coefficients

1. ## 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.)

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

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

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

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

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

Thanks.

2. 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.)

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

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

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

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

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

Thanks.
You have a typo in your characteristic equation. It should read

$\displaystyle m^2+6m+8=(m+2)(m+4)$

3. Originally Posted by TheEmptySet
You have a typo in your characteristic equation. It should read

$\displaystyle m^2+6m+8=(m+2)(m+4)$
Sorry. The typo was in the original equation. So it's still (m-2)(m-4).

4. Since the complimentary solution does not appear in the right hand side you can just "guess" the most simple form

$\displaystyle y=Ax^3+Bx^2+Cx+D+Me^{-2x}$