Verify that `y^(2) = 4(1-x^(2))` is a solution of the differential equation `xy y'' + x(y')^(2) - y y' = 0`

Explanation

To verify that \( y^2 = 4(1 - x^2) \) is a solution of the differential equation \( xy y'' + x(y')^2 - yy' = 0 \), we will follow these steps:

### Step 1: Differentiate \( y^2 = 4(1 - x^2) \)

We start by differentiating both sides with respect to \( x \):

\[
\frac{d}{dx}(y^2) = \frac{d}{dx}(4(1 - x^2))
...