2.3 Yk+1 - Yk = (n+ 1)k" The linear inhomogeneous difference equation Yk+1 – Yk (n + 1)k" (2.48) FIRST-ORDER DIFFERENCE EQUATIONS 51 can be written as Ayk = (n + 1)k", (2.49) where n is an integer....

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Extracted text: 2.3 Yk+1 - Yk = (n+ 1)k" The linear inhomogeneous difference equation Yk+1 – Yk (n + 1)k" (2.48) FIRST-ORDER DIFFERENCE EQUATIONS 51 can be written as Ayk = (n + 1)k", (2.49) where n is an integer. Consider the following equations and associated solutions: Ayk = 0, Yk = A; (2.50) %3D Ayk = 1, Yk = k + A; (2.51) Ayk = 2k, Yk = k² – k + A; Ayk = 3k2, Yk = k³ – 3/½ k² + /½ k + A; (2.52) (2.53) etc. In each case, A is an arbitrary constant. For n arbitrary, we have k-1 Yk = (n+ 1)A¬'(k") = (n + 1) i" + A, (2.54) %3D i=1