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

Understand the historical and contemporary context of food justice issues, including supermarket redlining and grocery access disparities.

Comprehend the strategies of coalition building among diverse groups to address common challenges and systemic issues.

Understand the concepts of opportunity recognition and idea generation within entrepreneurship.

Identify and differentiate between finding and effectuation approaches in opportunity creation.

---

Definitions:

Fixed Overhead

The set costs associated with operating a business that does not change in relation to production volume, such as rent, salaries, and insurance.

Administrative Costs

Expenses related to the general operations of a business, such as office supplies, management salaries, and utilities, which do not directly tie to specific product or service production.

Variable Manufacturing Costs

Costs that vary directly with the level of production, such as raw materials, direct labor, and certain overhead expenses.

Operating Income

Earnings before interest and taxes (EBIT), representing the profit from a company's core business operations.