Solve the following differential equation : `(1+"y"^2)(1+log"x")"dx"+"x\ dy"=0`

Explanation

To solve the differential equation \((1 + y^2)(1 + \log x)dx + x dy = 0\), we will use the method of separation of variables. Here’s a step-by-step solution:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ (1 + y^2)(1 + \log x)dx + x dy = 0 \]
We can rearrange this to isolate \(dy\):
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