Answer
$\dfrac{dy}{dx}=-(1+y) \sin x$ and $y(0)=2$
Work Step by Step
In order to determine the differential equation we will have to take the derivative of the differential equation.
Here, we have:
$\dfrac{dy}{dx}=-[1+y(x)] \sin x$
or, $\dfrac{dy}{dx}=-(1+y) \sin x$
Apply the initial conditions:
Then, we have $y(0)=2$
Hence, our answers are: $\dfrac{dy}{dx}=-(1+y) \sin x$ and $y(0)=2$
