Solve the Differential Equation Using the Method of Undetermined Coefficients $$y ^ { tt } - 5 y ^ { t } = \sin 15 x$$

question 16

Multiple Choice

Solve the differential equation using the method of undetermined coefficients. $$y ^ { tt } - 5 y ^ { t } = \sin 15 x$$

• A) \(y ( x ) = c _ { 1 } e ^ { 5 x } + \frac { 1 } { 250 } \cos ( 6 x ) + \frac { 1 } { 750 } \sin ( 6 x )\)
• B)\(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 5 x } + \frac { 1 } { 750 } \cos ( 6 x ) - \frac { 1 } { 250 } \sin ( 6 x )\)
• C) \(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 5 x } - \frac { 1 } { 250 } \sin ( 6 x )\)
• D)\(y ( x ) = c _ { 1 } e ^ { 5 x } + \frac { 1 } { 750 } \cos ( 6 x ) - \frac { 1 } { 250 } \sin ( 6 x )\)
• E)\(y ( x ) = \frac { 1 } { 750 } \cos ( 6 x ) - \frac { 1 } { 250 } \sin ( 6 x )\)

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Definitions:

Total Crash

In project management, it refers to the situation where the duration of a project is reduced to the minimum possible time by accelerating tasks at the highest cost increase.

Project Phases

The distinct stages a project goes through from initiation to completion, including planning, execution, and closure.

Crash Cost

The increased cost associated with reducing the completion time of a project task or activity beyond normal expectations.

Normal Duration

The standard amount of time typically expected for a particular task or activity to be completed under normal conditions.