Using the Method of Undetermined Coefficients, Determine the Most Suitable $y _ { p }$

question 31

Multiple Choice

Using the method of undetermined coefficients, determine the most suitable choice for $y _ { p }$ given $y ^ {tt } - 3 y ^ { t } - 54 y = x ^ { 2 }$ . (You do not need to solve the differential equation.)

• A) \(y _ { p } = A x + B\)
• B) \(y _ { p } = A x ^ { 2 } + B x + C\)
• C) \(y _ { p } = A x ^ { 3 } + B x ^ { 2 } + C x + D\)
• D) \(y _ { p } = A x ^ { 3 } + C x\)
• E) \(y _ { n } = A x ^ { 2 }\)

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Definitions:

Citric Acid Cycle

A key metabolic pathway that generates energy through the oxidation of acetate derived from carbohydrates, fats, and proteins into carbon dioxide and captures the released energy in the form of ATP.

Oxaloacetic Acid

A four-carbon molecule that plays a crucial role in both the Krebs cycle and gluconeogenesis, acting as a substrate for the generation of various intermediates.

Acetyl-CoA

A key molecule involved in metabolism that links glycolysis and the Krebs cycle, playing a crucial role in energy production.

Pyruvate

Pyruvate is a key intermediate in several metabolic pathways throughout the cell.