Solve the Differential Equation Using the Method of Variation of Parameters

question 61

Multiple Choice

Solve the differential equation using the method of variation of parameters.
Select the correct answer.
$$y ^ { tt } - y ^ { t } = e ^ { 2 x }$$

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

---

Definitions:

Engineering Change Order

A documented instruction that outlines the proposed changes in the details of an engineering project or product.

Product Change

The process of modifying or enhancing a product's features, design, or specifications to improve its appeal or functionality.

Process Change

Alteration or modification in the way a business operates, which could be due to technological advancements, compliance requirements, or operational improvement.

Desired Profit

The target earnings a company sets to achieve within a specific period through its operational activities.