To find the particular solution of the given differential equation using the Method of Undetermined Coefficients, the correct answer is option (b), which is yp = 313cos(3x) - 313sin(3x). So, the correct answer is option (b).
The question involves finding a particular solution, yp, of a second-order linear differential equation with constant coefficients using the Method of Undetermined Coefficients. The differential equation given is y'' - y' - 6y = 62cos(3x).
To determine the particular solution, we guess a solution of the form Acos(3x) + Bsin(3x), where A and B are coefficients to be determined.
Plugging the derivatives of the guessed solution into the given differential equation allows us to set up a system of equations. Solving for A and B involves comparing coefficients on both sides of the original equation.
After performing the necessary calculations, the correct particular solution is found to be yp = 313cos(3x) - 313sin(3x), which corresponds to option (b).
