Show that the given differential equation is homogeneous and solve each of them.`x^2(dy)/(dx)=x^2-2y^2+x y`

Explanation

To solve the differential equation \( x^2 \frac{dy}{dx} = x^2 - 2y^2 + xy \), we will first show that it is homogeneous and then find its solution.

### Step 1: Show that the differential equation is homogeneous

A function \( f(x, y) \) is homogeneous of degree \( n \) if \( f(\lambda x, \lambda y) = \lambda^n f(x, y) \) for any \( \lambda \).

Let's rewrite the equation:
\[
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