Question What is the form of the particular solution of the linear non-homogeneous recurrence relation an = 36an - 2 – 81an - 4 + F(n) if: (hint: the characteristic equation factorised is (x + 3)^(x – 3)2 (i) F(n) = 3 ii) F(n) = (n- 3)(-3)"
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Transcribed Image Text: What is the form of the particular solution of the linear non-homogeneous recurrence relation an = 36an - 2 – 81an - 4 + F(n) if: (hint: the characteristic equation factorised is (x + 3)^(x – 3)2 (i) F(n) = 3 ii) F(n) = (n- 3)(-3)"
More Transcribed Image Text: What is the form of the particular solution of the linear non-homogeneous recurrence relation an = 36an - 2 – 81an - 4 + F(n) if: (hint: the characteristic equation factorised is (x + 3)^(x – 3)2 (i) F(n) = 3 ii) F(n) = (n- 3)(-3)"
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Solution:- quada_(n)=36a_(n-2)-8∣a_(n)-4+F(n)Associated nomogencous recurrence relation.a_(n)=36a_(n-2)-81a_(n-4)Characteristic equation gamma^(4)=36gamma^(2)-81{:[gamma^(4)-36r^(2)+81=0],[(r^(2)-9)^(2)=0" or "(r^(2)-3)^(2)(r^(2)+3)^(2)=0],[{:[-3,3],[darr,__|],[2,2]:}]:}i) F(x)=3S=1 which i ... See the full answer