What is Particular solution of the recurrence ar+5ar-1+6ar-2=3r2
Answers
Answer:
6r = 10ar - 3
um..is this correct?
Answer:
Characteristic equation: r2 - 5r + 6 = 0, Solving the equation gives r = 2, 3.
Step-by-step explanation:
Step : 1 We identify a suitable trial solution. Let x1 and x2 be the roots of the related homogeneous recurrence relation, and let f(n)=cxn be the characteristic equation of the relation. If n=1, then a1=17a0+30 and a2=17a1+30*2. The result of substitution is a2=17(17a0+30)+60.
Step : 2 Since the differential equation contains no arbitrary variables, the specific solution may be easily determined. The answers y = 3x + 3 and y = x2 + 11x + 7 are examples of specific differential equation solutions. With starting conditions a0 = 1 and a1 = 6, solve the recurrence relation a = 6an-1 9an-2. These equations may be solved to provide 1 = 1 and 2 = 1. Consequently, a = 3n + n3n.
Step : 3 A1=2A0+3 when n=1, and a2=2A1+3 now. A2=2(2a0+3)+3 is the result of substitution. When the words are regrouped, we obtain a4=141, where a0=6. It is important to note that if a = 2n for every n, then 8an1 16an2 = 8(2n1)16(2n2)=4 This sequence is not a solution to the stated recurrence relation since 22n1442n2 = 42n42n = 0 = an.
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