Solve the Differential Equation $$y ^ { t } = x ^ { 2 } e ^ { - \sin x } - y \cos x$$

question 17

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ { t } = x ^ { 2 } e ^ { - \sin x } - y \cos x$$

• A) \(y = 2 \mathrm { Ce } e ^ { - \sin x }\)
• B) \(y = e ^ { - \sin x } + 2 C x ^ { 2 }\)
• C)
• \(y = \frac { 1 } { 3 } x + C e ^ { - \cos x }\)
• D) \(y = \left( 3 x ^ { 3 } + C \right) e ^ { - x } \sin x\)
• E)
• \(y = \left( \frac { 1 } { 3 } x ^ { 3 } + C \right) e ^ { - \sin x }\)

Understand the short-run and long-run market equilibrium changes due to shifts in market demand and supply in competitive industries.

Identify the factors leading to entry and exit of firms in a competitive market.

Recognize the characteristics of a perfectly competitive market, including demand curve elasticity.

Grasp the concept of economic profits and how they approach zero in the long run in competitive markets.

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A concept in economics where a country can produce a particular good or service at a lower opportunity cost than its trading partners.