Solve the Differential Equation $$y ^ {tt } - 8 y ^ { t } + 41 y = 0$$

question 102

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ {tt } - 8 y ^ { t } + 41 y = 0$$

• A) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 5 x ) + c _ { 2 } x \sin ( 5 x ) \right)\)
• B) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 5 x ) + c _ { 2 } \sin ( 5 x ) \right)\)
• C) \(y ( x ) = e ^ { 5 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } \sin ( 4 x ) \right)\)
• D) \(y ( x ) = c e ^ { 4 x } \cos ( 5 x )\)
• E) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)\)

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Definitions:

Hermann von Helmholtz

A German physician and physicist who made significant contributions to the understanding of the physiology of vision, hearing, and electromagnetism.

Basilar Membrane

A core component of the cochlea in the inner ear, playing a crucial role in the sense of hearing by vibrating in response to sound.

Ossicles

Three small bones in the middle ear known as the malleus, incus, and stapes, crucial for transmitting sound vibrations to the inner ear.

Middle Ear

The section of the ear located between the eardrum and the inner ear, containing the ossicles, which transmit sound vibrations to the inner ear.