Question

If yₚ=Ax²+Bx+C is a particular solution of the DEy''−2y′+y=x² +x the A+B+C=

a. -2
b. 2
c. 14
d. 1

Answer 1

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.