Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:`y=sqrt(a^2-x^2)x in (-x , a)` : `x+y(dy)/(dx)=0(y!=0)`

Explanation

To verify that the function \( y = \sqrt{a^2 - x^2} \) is a solution of the differential equation \( x + y \frac{dy}{dx} = 0 \), we will follow these steps:

### Step 1: Differentiate the function
We start with the function:
\[ y = \sqrt{a^2 - x^2} \]
Now, we differentiate \( y \) with respect to \( x \):
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