Solve the First Order Linear Differential Equation $$\frac { d y } { d x } + \frac { 8 } { x } y = 7 x + 2$$

question 4

Multiple Choice

Solve the first order linear differential equation. $$\frac { d y } { d x } + \frac { 8 } { x } y = 7 x + 2$$

• A) \(y = \frac { 7 } { 10 } x ^ { 2 } - \frac { 2 } { 9 } x + C x ^ { - 8 }\)
• B) \(y = \frac { 10 } { 7 } x ^ { 2 } + \frac { 9 } { 2 } x + C x ^ { - 8 }\)
• C) \(y = - \frac { 7 } { 10 } x ^ { 2 } + \frac { 2 } { 9 } x + C x ^ { - 8 }\)
• D) \(y = - \frac { 10 } { 7 } x ^ { 2 } + \frac { 9 } { 2 } x + C x ^ { - 8 }\)
• E) \(y = \frac { 7 } { 10 } x ^ { 2 } + \frac { 2 } { 9 } x + C x ^ { - 8 }\)

---

Definitions:

Specific Tax

A tax that is levied as a fixed amount per unit of a good or service, rather than a percentage of the price.

Elasticity of Supply

A measure of how much the quantity supplied of a good responds to a change in the price of that good, indicating the flexibility of producers.

Deadweight Loss

An economic inefficiency resulting from the lack of or impossibility to attain equilibrium in the market for a particular good or service.

Tax Revenue

The income generated by the government through the imposition of taxes on goods, services, and income.