Solve the Differential Equation Using the Method of Variation of Parameters

question 99

Multiple Choice

Solve the differential equation using the method of variation of parameters.
$$y ^ { tt } - 4 y ^ { t } + 3 y = 3 \sin x$$

• A)
• \(y ( x ) = c _ { 1 } \sin 3 x + \frac { c _ { 2 } } { 4 } x + \cos 3 x\)
• B)
• \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 5 } \cos x + \frac { 3 } { 10 } \sin x\)
• C)
• \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 5 } \sin x\)
• D)
• \(y ( x ) = c _ { 1 } \sin x + \frac { c _ { 2 } } { 5 } x + \frac { 3 } { 10 } \sin x\)
• E)
• \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 10 } \sin x\)

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Definitions:

Rand()

A function in many programming languages used to generate a pseudo-random number within a specified range.

Time()

A function in many programming languages that returns the current time, often represented as the number of seconds since a predefined epoch.

Scaling

Scaling refers to the process of adjusting the size or capacity of a system or application to handle varying levels of demand.

Random Number

A number generated in such a way as to exhibit no predictable pattern or order, often used in computing to simulate chance or create variability in data processing.