Using Power Series Methods, the Solution Of $x y ^ { \prime \prime } - x y ^ { \prime } + y = 0$

question 36

Multiple Choice

Using power series methods, the solution of $x y ^ { \prime \prime } - x y ^ { \prime } + y = 0$ is

• A) \(y = c _ { 0 } x + c _ { 1 } \left[ x \ln x - 1 + \sum _ { n = 2 } ^ { \infty } x ^ { n } / n ! \right]\)
• B) \(y = c _ { 0 } x + c _ { 1 } \left[ x \ln x - 1 + \sum _ { n = 1 } ^ { \infty } x ^ { n } / ( n ! ( n + 1 ) ) \right]\)
• C) \(y = c _ { 0 } x + c _ { 1 } \left[ x \ln x + \sum _ { n = 2 } ^ { \infty } x ^ { n } / ( n ! ( n - 1 ) ) \right]\)
• D) \(y = c _ { 0 } x + c _ { 1 } \left[ x \ln x + \sum _ { n = 1 } ^ { \infty } x ^ { n } / ( n ! ( n - 1 ) ) \right]\)
• E) \(y = c _ { 0 } x + c _ { 1 } \left[ x \ln x - 1 + \sum _ { n = 2 } ^ { \infty } x ^ { n } / ( n ! ( n - 1 ) ) \right]\)

---

Definitions:

Electrocardiograph

A medical device used to record the electrical activity of the heart over a period of time.

Sympathetic Division

Part of the autonomic nervous system responsible for the body's 'fight or flight' response, activating physiological changes during times of stress or emergency.

Parasympathetic Division

A branch of the autonomic nervous system responsible for 'rest and digest' activities, slowing down the body after stress or exertion.

Intense Arousal

A heightened state of physiological activity and alertness, often associated with emotions such as excitement, anxiety, or fear.