Final answer:
To solve the given differential equation using undetermined coefficients, first find the complementary solution and then the particular solution. The general solution is a combination of the complementary solution and particular solution.
Step-by-step explanation:
To solve the given differential equation using undetermined coefficients, we first find the complementary solution by setting the right-hand side to zero. The characteristic equation is r^2 - 12r + 36 = 0, which factors to (r - 6)^2 = 0. Therefore, the complementary solution is y_c = (c1 + c2x)e^(6x).
To find the particular solution, we let y_p = Ax + B be a linear function since the right-hand side is a linear function. Substituting y_p back into the differential equation, we find that A = 1 and B = 7.
Therefore, the general solution is y = (c1 + c2x)e^(6x) + x + 7.