Show that the differential equation

$xdxydy=0$

is exact.

$2.$ Find the general solution of this exact differential equation and describe the family of curves.

$3.$ Note that we can rewrite the exact equation as $\frac{dy}{dx}=-\frac{x}{y}.$ Now write an ODE whose solution is the family of curves orthogonal to the circles you found in part $2.$ Solve this new ODE.

$4.$ Sketch some solutions for each ODE on the same set of axes.

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