Find Constants a and B So That the Given Expression $y _ { n }$

question 4

Multiple Choice

Find constants A and B so that the given expression $y _ { n }$ satisfies the specified difference equation. $n ^ { 2 } y _ { n } + n y _ { n - 1 } = 4 n - 2 n ^ { 3 } ; y _ { n } = A n + B$

• A) \(A = 2 , B = 2\)
• B) \(A = - 2 , B = - 2\)
• C) \(A = 2 , B = - 2\)
• D) \(A = - 2 , B = 2\)

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Definitions:

Figure

An object's shape, outline, or representation in art or mathematics, or a notable person in a particular field.

Syllogism

A form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises); a logical structure that uses three parts.

Middle Term

In a categorical syllogism, the term that appears in both premises and links together the major and minor terms.

Syllogism

A form of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.