Introduction to Difference Equations Problems 3.4, p. 147, #1-3

(d) y_k+2 - y_k+1 - 2y_k = k²

Characteristic equation (auxiliary equation)

Roots of the characteristic equation

General solution of the homogeneous equation

#1: Particular solution of the nonhomogeneous equation

#2: General solution of the nonhomogeneous equation

#3: Solve the initial-condition equations for the constants in the general solution.

Solution of the given nonhomogeneous equation satisfying the given initial conditions

Check: Compare values of y_k for the recurrence with initial conditions with the values of your solution for k = 0, 1, 2, 3.