Explain the determine Difference EquationsExample EConsider the third-order difference equation7yk+2 + 16yk+1 – 12yk = k2*.(4.174)Yk+3Its characteristic equation ispi3 – 7n2 + 16r – 12 = (r – 2)2 (r – 3) = 0,(4.175)%3Dand the corresponding homogeneous solution is(Н)= (c1 + c2k)2* + c33*,(4.176)k2k iswhere c1, c2, and c3 are arbitrary constants. The family of Rk[2k, k2k]. Note that both members occur in the homogeneous solution; there-fore, we must multiply the family by k? to obtain a new family that doesnot contain any function that appears in the homogeneous solution. The newfamily is [k?2*, k³2*]. Thus, the particular solution isP) = (Ak² + Bk³)2*,(4.177)where A and B are to be determined. The substitution of equation (4.177)into equation (4.174) gives2* (-8A+24B) + k2* (-24B) = k2*,(4.178)or8A – 24B = 0,-24B = 1,(4.179)andА-1/s,B = -/24.(4.180)Therefore, the particular solution is(P):-/24(3 + k)k²2*,(4.181)and the general solution isYk = (c1 + c2k)2k + c33k – 1/24(3+ k)k²2*.(4.182)

Name: Explain the determine Difference EquationsExample EConsider the third-
Uploaded: 2024-03-20T06:47:08.000Z
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Description: Explain the determine Difference EquationsExample EConsider the third-order difference equation7yk+2 + 16yk+1 – 12yk = k2*.(4.174)Yk+3Its characteristic equation ispi3 – 7n2 + 16r – 12 = (r – 2)2 (r – 3) = 0,(4.175)%3Dand the corresponding homogeneou