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Slope Fields of the equation dy/dx=x/y on the point (3,-1) and (1,2)

By Emma Terry
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In this question, I am meant to draw the solution curves that pass through the two points.

This is my work: enter image description here

However, after solving the differential equation, I found out that it is a hyperbola. Does this mean for the solution curve I should draw a curve that mirrors the curve that have already been drawn or not or should I only keep the curves that pass through the respective points?

Thank you very much.

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