Final answer:
The question pertains to solving a second-order linear nonhomogeneous differential equation using undetermined coefficients to find the particular solution that includes a sinusoidal nonhomogeneous term.
Step-by-step explanation:
The subject of this question is to use the method of undetermined coefficients to find the particular solution of the second-order linear nonhomogeneous differential equation y'' + y' - 20y = -1326sin(t).
To solve this, we'll need to address the homogeneous part first, which is y'' + y' - 20y = 0, and find its general solution. Then, we can guess a particular solution for the nonhomogeneous part, which is typically of the form A sin(t) + B cos(t) because the nonhomogeneous term is a sine function.
Afterward, we substitute our assumed particular solution into the differential equation and solve for A and B. Lastly, we combine the general solution of the homogeneous equation with the particular solution to get the complete solution.