The Correct Form of the Particular Solution Of $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$

question 15

Multiple Choice

The correct form of the particular solution of $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$ is

• A) \(y _ { p } = A e ^ { - x }\)
• B) \(y _ { p } = A x e ^ { - x }\)
• C) \(y _ { p } = A x ^ { 2 } e ^ { - x }\)
• D) \(y _ { p } = A x ^ { 3 } e ^ { - x }\)
• E) none of the above

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Definitions:

Collagen Fibers

Strong, flexible proteins found in connective tissues, such as skin, tendons, and ligaments, providing structural support.

Synovial Joints

Joints that are surrounded by a fluid-filled capsule, allowing for smooth movement between connected bones.

Syndesmosis

A type of fibrous joint in which bones are joined together by a ligament or a membrane, allowing for minimal movement.

Gomphosis

A type of fibrous joint where a peg-like structure fits into a socket, such as a tooth in the jawbone.