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A particle moves along a certain curve in such a way that its tangent slope is always equal to $6xy$.

If the particle passes through the point $(0, \,3)$, determine the equation of the particle's path.

A

$y = \sqrt {6x^2 + 9}$

B

$y=3e^{3x^2}$

C

$y=e^{3x^2}+2$

D

$y = 6x^2 + 3$

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