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

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

Correct Answer:

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