The Solution Of $y ^ { \prime \prime } + 4 y ^ { \prime } + 4 y = 0$

question 17

Multiple Choice

The solution of $y ^ { \prime \prime } + 4 y ^ { \prime } + 4 y = 0$ is

• A) \(y = c _ { 1 } e ^ { - 2 x } + c _ { 2 } x e ^ { - 2 x }\)
• B) \(y = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 2 x }\)
• C) \(y = c _ { 1 } e ^ { 2 x } + c _ { 2 } e ^ { 2 x }\)
• D) \(y = c _ { 1 } e ^ { 2 x } + c _ { 2 } x e ^ { 2 x }\)
• E) \(y = c _ { 1 } e ^ { 2 x } + c _ { 2 } e ^ { 4 x }\)

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Definitions:

Fixed Costs

Fixed costs are expenses that remain constant for a company regardless of how much it produces or sells, such as rent, salaries, and insurance premiums.

Variable Costs

Costs that fluctuate in direct proportion to the amount of production or sales figures.

Fixed Costs

Overhead expenses that remain consistent regardless of changes in the level of production or sales activities.