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) \(\frac { 1 } { 2 } \sin \left( x ^ { 2 } \right) + \frac { 1 } { 2 }\)

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