Solve the First Order Linear Differential Equation $y ^ { \prime } - 2 x y = e ^ { x ^ { 2 } }$

question 50

Multiple Choice

Solve the first order linear differential equation. $y ^ { \prime } - 2 x y = e ^ { x ^ { 2 } }$

• A) \(y = e ^ { x ^ { 2 } } ( 2 x + C )\)
• B) \(y = e ^ { x ^ { 2 } } ( x + C )\)
• C) \(y = e ^ { x ^ { 2 } } ( 3 x + C )\)
• D) \(y = e ^ { x ^ { - 2 } } ( x + C )\)
• E) \(y = e ^ { x ^ { - 2 } } \left( x + C ^ { x } \right)\)

---

Definitions:

Psychodynamic Theory

A psychological perspective that emphasizes the influence of the unconscious mind and childhood experiences on behavior and personality.

Evolutionary Theory

A scientific explanation for the diversity of life on Earth, proposing that species change over time through processes like natural selection and genetic mutation.

Masculinity and Femininity

Socially constructed roles, behaviors, expressions, and identities associated with being male or female, varying across different cultures and times.

Genetic Sex

Determined by the chromosomes an individual inherits, typically XX for females and XY for males, influencing primary and secondary sex characteristics.