Final answer:
To find the values of A, B, and C in a particular solution of the differential equation y'' - 2y' + y = x² + x, substitute the quadratic equation yₚ = Ax² + Bx + C into the differential equation and solve for A, B, and C. The given answer choices do not directly represent the solution to A + B + C.
Step-by-step explanation:
To find the values of A, B, and C in a particular solution of the differential equation y'' - 2y' + y = x² + x, we can substitute the quadratic equation yₚ = Ax² + Bx + C into the differential equation and solve for A, B, and C.
Substituting yₚ into the differential equation, we get:
A(2) - 2A + A - 2B + C = x² + x
Simplifying this equation, we get:
2A - 2B + C = x² + x
From the given answer choices, we can see that none of them directly represent the solution to A + B + C. Therefore, the answer is not provided in the given options.