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)
• \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 10 } \sin x\)

---

Definitions:

Suicide Cluster

When two or more suicides or attempted suicides nonrandomly occur closely together in space or time.

Attempted Suicides

Instances where individuals try to take their own lives but do not succeed.

Nonrandomly

A selection or occurrence method that is not based on chance, often implying bias or a predetermined pattern.

Émile Durkheim

A founding figure in sociology, known for his work on social integration, religion, and theories on the collective conscience and anomie.