Solve the following differential equation: `(y+x y)dx+(x-x y^2)dy=0`

Explanation

To solve the differential equation \((y + xy)dx + (x - xy^2)dy = 0\), we will follow a systematic approach.

### Step 1: Rearranging the Equation
First, we can rearrange the equation to separate the variables. We can write it as:
\[ (y + xy)dx + (x - xy^2)dy = 0 \]
This can be rearranged to:
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