Chapter 9: First-Order Differential Equations - Section 9.1 - Solutions, Slope Fields, and Euler's Method - Exercises 9.1 - Page 531: 9

$\dfrac{dy}{dx}=-(1+y) \sin x$ and $y(0)=2$

Take derivative of the given differential equation. This implies that $\dfrac{dy}{dx}=-[1+y(x)] \sin x$ or, $\dfrac{dy}{dx}=-(1+y) \sin x$ Now, apply the initial conditions, Thus, we get $y(0)=2$