3.4.1 Example A An easy calculation shows that y0 = 2*, Yk (1) %3D (2) = 1 (3.77) are solutions to the homogeneous equation Yk+2 3yk+1+2yk = 0. (3.78) Furthermore, their Casoratian is given by the following expression: 2k+1 1 2k+2 1 C(k + 1) = -2k+1. (3.79) = Let us use these results to calculate a particular solution to the inhomo- geneous equation Yk+2 - 3yk+1 + 2yk 4* + 3k2. (3.80) Let Y be the particular solution, where Yk = C1(k)2* + C2(k). (3.81) The functions C1(k) and C2(k) satisfy the following equations: 2k+1AC1(k) + AC2(k) = 0, %3D (3.82) 2*+2AC1 (k) + AC2(k) = 4* + 3k2.

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