Solve the differential equation `x(dy)/(dx)+coty=0,` given that `y=pi/4` , when `x=sqrt(2)`

Explanation

To solve the differential equation \( x \frac{dy}{dx} + \cot y = 0 \) with the initial condition \( y = \frac{\pi}{4} \) when \( x = \sqrt{2} \), we will follow these steps:

### Step 1: Rearranging the Differential Equation
We start with the given equation:
\[ x \frac{dy}{dx} + \cot y = 0 \]
Rearranging gives:
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