Step 1 :1. \(v(x) = \frac{y(x)}{\sin(x)} \)
Step 2 :2. \(v'(x) = \frac{y'(x) \sin(x) - y(x) \cos(x)}{\sin^2(x)} \)
Step 3 :3. \(v'(x) = \frac{\sin^3(x)}{(1 + \sin x + \cos x) \sin^2(x)} \)
Step 4 :4. Integrate \(v'(x)\): \(v(x) = \int \frac{\sin^3(x)}{(1 + \sin x + \cos x) \sin^2(x)} dx + C \)
Step 5 :5. \(y(x) = v(x) \sin(x) = \sin(x) \left(\int \frac{\sin^3(x)}{(1 + \sin x + \cos x) \sin^2(x)} dx + C\right) \)