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\begin{center}
\textbf{Vector Fields}

\textit{\textbf{Scalar and Vector Fields}}
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\textbf{Question}

Describe the streamlines of the following velocity field.

$\un{v}(x,y) = x^2\un{i} -y\un{j}$


\textbf{Answer}

The field lines satisfy $\frac{dx}{x^2} = -\frac{dy}{y}$.

So they are given by $\ln |y| = \frac{1}{x} + \ln |C|$, or
equivalently, $y=Ce^{1/2}$.

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