Without Solving for the Undetermined Coefficients, the Correct Form of a Particular

question 31

Multiple Choice

Without solving for the undetermined coefficients, the correct form of a particular solution of the differential equation $y ^ { \prime \prime } + 4 y ^ { \prime } + 5 y = e ^ { - 2 x } \cos x$ is

• A) \(y _ { p } = A e ^ { - 2 x } \cos x\)
• B) \(y _ { p } = A e ^ { - 2 x } \cos x + B e ^ { - 2 x } \sin x\)
• C) \(y _ { p } = A e ^ { - 2 x } \sin x\)
• D) \(y _ { p } = A x e ^ { - 2 x } \cos x + B x e ^ { - 2 x } \sin x\)
• E) \(y _ { p } = A x e ^ { - 2 x } \cos x + B e ^ { - 2 x } \sin x\)

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Definitions:

Positive Reinforcers

In behavioral psychology, stimuli that, when presented following a behavior, increase the likelihood of that behavior being repeated.

Negative Reinforcers

In behavioral psychology, an unpleasant stimulus whose removal leads to an increase in the likelihood that a preceding behavior will be repeated in the future.

Negative Reinforcement

A type of operant conditioning that strengthens a behavior by removing an unpleasant stimulus when the behavior occurs.

Tertiary Reinforcement

A form of reinforcement where a stimulus gains its reinforcing power through association with a secondary reinforcer, rather than satisfying a basic biological need.