FIRST-ORDER DIFFERENCE EQUATIONS 53 2.3.1 Example The equation Yk+1 – Yk = 1 - k+ 2k3 (2.62) has the particular solution k-1 k-1 k-1 k-1 Σ1-i+2) - Σ (1) -Σι+2Σε Yk = i=1 (2.63) i=1 i=1 i=1 k(k – 1) (k...

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Extracted text: FIRST-ORDER DIFFERENCE EQUATIONS 53 2.3.1 Example The equation Yk+1 – Yk = 1 - k+ 2k3 (2.62) has the particular solution k-1 k-1 k-1 k-1 Σ1-i+2) - Σ (1) -Σι+2Σε Yk = i=1 (2.63) i=1 i=1 i=1 k(k – 1) (k – 1)²k² = (k – 1) – 2 The general solution is Yk = /2k* – k3 + 3/2k + A, (2.64) where A is an arbitrary constant. In terms of Bernoulli polynomials, this last expression reads Yk = B1(k) – 1/2B2(k)+\/½B4(k) + A1, (2.65) where A1 is an arbitrary function.