Solution of the differential equation `cosx dy= y(sinx -y)dx , 0 lt x lt pi/2` (A) `secx=(tanx+c)y` (B) `ysecx=tanx+c` (C) `ytanx=secx+c` (D) `tanx=(secx+c)y`

Explanation

To solve the differential equation \( \cos x \, dy = y(\sin x - y) \, dx \) for \( 0 < x < \frac{\pi}{2} \), we can follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ \cos x \, dy = y(\sin x - y) \, dx \]
Dividing both sides by \( \cos x \) and \( y \):
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