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
Instead of memorizing formula's, you could do the following.
First, the complementary . As you said, the roots are 1, 1 so
For the particular, ask is the nonhomogenous part contained in the complementary solution - no. So seek a particular solution of the form
Substitute gives
Comparing gives A = -7 and B = 0 so
and the solution