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

question 5

Multiple Choice

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

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

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Definitions:

Behavioral Therapy

A treatment approach that focuses on modifying negative behaviors through reinforcement methods.

Cognitive Therapy

A therapy developed by Aaron Beck that helps people identify and change the maladaptive assumptions and ways of thinking that help cause their psychological disorders.

Sociocultural Therapy

A therapeutic approach that emphasizes the influence of society, culture, and family on individual mental health, focusing on how social and cultural factors contribute to psychological problems.

Psychodynamic Approaches

A category of psychotherapy that emphasizes the psychological forces underlying human behavior, feelings, and emotions, often exploring childhood experiences.