Show that `y^(2)dx + (xy + x^(2))dy = 0` is a homogeneous differential equation. Also find its general solution.

Explanation

To show that the differential equation \( y^2 dx + (xy + x^2) dy = 0 \) is a homogeneous differential equation and to find its general solution, we will follow these steps:

### Step 1: Check if the equation is homogeneous
A differential equation is homogeneous if it can be expressed in the form \( M(x, y)dx + N(x, y)dy = 0 \) where \( M \) and \( N \) are homogeneous functions of the same degree.

Here, we have:
- \( M(x, y) = y^2 \)
- \( N(x, y) = xy + x^2 \)
...