I am just wanting somebody to check my work.

5. Find the Particular solution of the following equation using Undetermined Coefficients(yparticular(t). $\displaystyle y''-2y'+y=7e^t cos(t)$

The auxiliary equation I get is:

$\displaystyle r^2-2r+1=0$

$\displaystyle (r-1)^2=0$

$\displaystyle r=1$ Twice

So,

$\displaystyle \alpha = \frac2 2 = 1$

$\displaystyle \beta = \sqrt(4-4)/2) = 0$

That means that s=1

So the equation I get is:

$\displaystyle yparticular(t)=t*A*t^0*e^t*cos(0*t)+t*B*t^0*e^t*sin(0*t)$

which simplifies to

$\displaystyle y(t)=A*t*e^t$