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

question 8

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

---

Definitions:

Esker

A long, winding ridge of stratified sand and gravel, typically occurring in glaciated and formerly glaciated regions, formed by retreating glaciers or meltwater.

Levees

Natural or artificial embankments built along rivers or watercourses to prevent their waters from overflowing onto adjacent land.

Flooding

The overflow of water onto land that is normally dry, often caused by heavy rain, melting snow, or storm surges.

Constructed

Made, built, or put together using various parts or materials, often referring to buildings, roads, or other engineered structures.