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

question 16

Multiple Choice

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

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

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Definitions:

Outer Ear

The outer ear is the external part of the ear, consisting of the pinna and the ear canal, which collects sound waves and directs them into the ear.

Middle Ear

The portion of the ear internal to the eardrum and external to the cochlea, containing three small bones that amplify sound vibrations.

Inner Ear

The innermost part of the ear, containing the cochlea, vestibule, and semicircular canals, which are responsible for sound detection and balance.