Solve the Differential Equation $$y ^ { tt } - 4 y ^ { t } + 20 y = 0$$

question 43

Multiple Choice

Solve the differential equation. $$y ^ { tt } - 4 y ^ { t } + 20 y = 0$$

• A) \(y ( x ) = e ^ { 2 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } \sin ( 4 x ) \right)\)
• B) \(y ( x ) = e ^ { 2 x } \left( c _ { 1 } \cos ( 2 x ) + c _ { 2 } x \sin ( 2 x ) \right)\)
• C) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 2 x ) + c _ { 2 } \sin ( 2 x ) \right)\)
• D) \(y ( x ) = \operatorname { ce } 2 x \cos ( 4 x )\)
• E) \(y ( x ) = e ^ { 2 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)\)

---

Definitions:

Monopolistic Competition

A market structure characterized by many firms selling similar but not identical products, with each having some control over its own prices.

Price Makers

Entities in a market that have the power to set prices for goods or services because they hold significant control over the market or the product.

Oligopoly

A market structure in which a small number of firms dominate the market, leading to limited competition and possibly higher prices for consumers.

Market Power

The ability of a firm or group of firms to influence or control prices and total market output.