Find the Solution of the Initial-Value Problem $\frac { d y } { d x } = x \sin \left( x ^ { 2 } \right)$

question 127

Multiple Choice

Find the solution of the initial-value problem $\frac { d y } { d x } = x \sin \left( x ^ { 2 } \right)$ , $y ( 0 ) = 0$ .

• A) \(- \frac { 1 } { 2 } \cos \left( x ^ { 2 } \right) - \frac { 1 } { 2 }\)
• B) \(- \frac { 1 } { 2 } \cos \left( x ^ { 2 } \right)\)
• C) \(- \frac { 1 } { 2 } \cos \left( x ^ { 2 } \right) + \frac { 1 } { 2 }\)
• D) \(\frac { 1 } { 2 } \cos \left( x ^ { 2 } \right) + \frac { 1 } { 2 }\)
• E) \(- \frac { 1 } { 2 } \sin \left( x ^ { 2 } \right) - \frac { 1 } { 2 }\)
• F) \(- \frac { 1 } { 2 } \sin \left( x ^ { 2 } \right)\)
• G) \(- \frac { 1 } { 2 } \sin \left( x ^ { 2 } \right) + \frac { 1 } { 2 }\)
• H) \(\frac { 1 } { 2 } \sin \left( x ^ { 2 } \right) + \frac { 1 } { 2 }\)

---

Definitions:

Fraternal Twins

Twins that develop from two different eggs fertilized by two different sperm cells, genetically similar like regular siblings.

Heritability Ratio

The Heritability Ratio is a measure in genetics quantifying how much of a trait's variation within a population is due to genetic factors.

Trait Variability

The degree to which individuals exhibit differences in their characteristics or behaviors.

Genetic Inheritance

The process by which genetic information is passed on from parents to their offspring, influencing traits and susceptibility to certain diseases.