Solve the Differential Equation Using the Method of Variation of Parameters

question 31

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:

College Graduates

Individuals who have completed a college degree program at an accredited institution of higher education.

Job Market

The marketplace in which employers seek employees and employees seek jobs; reflects the dynamics of demand and supply for labor.

High School Dropouts

High School Dropouts refer to individuals who do not complete their secondary education or obtain a high school diploma.

Middle-And Working-Class

Social groups typically defined by their occupational roles, income levels, and educational attainment, often considered the backbone of economic and productive activities in a society.