A particle moves in the plane \( x y \) with velocity \( \mathbf{v}=a \mathbf{i}+b x \mathbf{j} ...

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A particle moves in the plane \( x y \) with velocity \( \mathbf{v}=a \mathbf{i}+b x \mathbf{j} \), where \( \mathbf{i} \) and j are the unit vectors of the \( x \) and \( y \) axes, and \( a \) and \( b \) are constants. At the initial moment of time the particle wave located at the point \( x=y=0 \). Find :
the equation of the particle's trajectory \( y(x) \);
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