Solve the Differential Equation $$y ^ { tt } - 4 y ^ { t } + 20 y = 0$$

question 111

Multiple Choice

Solve the differential equation.
$$y ^ { tt } - 4 y ^ { t } + 20 y = 0$$

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

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Definitions:

Component Reliabilities

Measures of a component's ability to perform its required function under stated conditions for a specified period.

Reliable Backup

A dependable system or process that can be used as an alternative in case the primary system fails.

Infant Mortality

A term used in reliability engineering to describe a phenomenon where a product or system has a high failure rate early in its operational life.

Electronics

The branch of physics and engineering dealing with the emission, behavior, and effects of electrons in vacuum, gases, and semiconductors, and with electronic devices.