Solve the differential equation `x y(dy)/( dx)=(1+y^2)/(1+x^2)(1+x+x^2)`

Explanation

To solve the differential equation \( x y \frac{dy}{dx} = \frac{1 + y^2}{(1 + x^2)(1 + x + x^2)} \), we will follow these steps:

### Step 1: Separate the Variables
We start by rearranging the equation to separate the variables \( y \) and \( x \):
\[ x y \frac{dy}{dx} = \frac{1 + y^2}{(1 + x^2)(1 + x + x^2)} \]
This can be rewritten as:
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