Solve the Initial-Value Problem $$y ^ { tt } + 3 y ^ { t } - 4 y = 0 , y ( 0 ) = 2 , y ^ { t } ( 0 ) = 1$$

question 59

Multiple Choice

Solve the initial-value problem. $$y ^ { tt } + 3 y ^ { t } - 4 y = 0 , y ( 0 ) = 2 , y ^ { t } ( 0 ) = 1$$

• A)\(y = e ^ { 2 x } + \frac { 1 } { 5 } e ^ { - 2 x }\)
• B) \(y = \frac { 9 } { 5 } e ^ { x } + \frac { 1 } { 5 } e ^ { - 4 x }\)
• C) \(y = \frac { 1 } { 5 } e ^ { 2 x } + \frac { 9 } { 5 } e ^ { - 2 x }\)
• D) \(y = e ^ { x } + \frac { 1 } { 5 } e ^ { - 3 x }\)
• E) None of these

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Definitions:

Ego

The conscious part of the mind that navigates between the id and the super-ego.

Psychodynamic Theorists

Individuals in psychology who study and apply theories focused on the unconscious mind's influence over human behavior and emotions.

Interplay

The reciprocal influence or interaction between two or more factors, highlighting how they affect each other in various contexts.

Conscious

The part of the mind within our usual awareness.