Find the exact solution for the following differential equation using the method of undetermined coefficients: y``-4y`+3y=18t+6, e^(3t), with initial conditions y(0)=2 and y`(0)=13. Which of the following options represents the correct solution?
A) y(t) = 3t2 + 2t + 1
B) y(t) = 6t + 2
C) y(t) = 9t2 + 2t + 1
D) y(t) = 12t + 2
