Systems of Differential Eq (Undetermined Coefficients)

[champ2029]

Hello guys,

I need help solving this problem.

Find the particular solution using method of undetermined coefficients:

X'=AX + F(t)

A= [4 ,1/3] <-- 1st row
[9 , 6] <-- 2nd row

F(t) = [-e^t,e^t]

The complementary function is Xc=c1[1,3]e^(3t) + c2[1,9]e^(7t)

Any help would be greatly appreciated!

 

[champ2029]

Repost. Sorry if things aren't clear. Here are the given using latex

A=\begin{pmatrix}4 & 1/3\\ 9 & 6\end{pmatrix}

F(t)=\begin{pmatrix}-e^t\\ e^t\end{pmatrix}

$Xc=c1\begin{pmatrix}1\\ 3\end{pmatrix}e^3t + c2\begin{pmatrix} 1\\ 9\end{pmatrix}e^7t$

I'm having trouble finding the particular solution for the problem because F(t) is in exponential form. Please teach me how to approach this problem