I am just wanting somebody to check my work.

5. Find the Particular solution of the following equation using Undetermined Coefficients(yparticular(t).

The auxiliary equation I get is:

Twice

So,

That means that s=1

So the equation I get is:

particular(t)=t*A*t^0*e^t*cos(0*t)+t*B*t^0*e^t*sin(0*t)" alt="yparticular(t)=t*A*t^0*e^t*cos(0*t)+t*B*t^0*e^t*sin(0*t)" />

which simplifies to