Solve the Initial-Value Problem $$y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 4$$

question 44

Multiple Choice

Solve the initial-value problem. Select the correct answer.
$$y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 4$$

• A)
• \(y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 8 } { 5 } \sin ( 5 x ) \right)\)
• B)
• \(y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• C)
• \(y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 8 } { 5 } \sin ( 4 x ) \right)\)
• D)
• \(y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• E)
• \(y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 8 } { 5 } \sin ( 5 x ) \right)\)

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Definitions:

Amphibians

A group of cold-blooded vertebrates characterized by their ability to live both in water and on land, undergoing metamorphosis from a larval stage to an adult.

Carboniferous

A geologic period and system that extends from the end of the Devonian Period, about 359.2 million years ago, to the beginning of the Permian Period, about 299 million years ago.

Reptiles

Cold-blooded vertebrates that breathe air, usually lay eggs, and have scales covering their bodies, including snakes, lizards, crocodiles, and turtles.

Chordates

Deuterostome animals that, at some time in their lives, have a cartilaginous, dorsal skeletal structure called a notochord; a dorsal, tubular nerve cord; pharyngeal slits; a postanal tail; and an endostyle (or its derivative, a thyroid gland).