Chapter 9: First-Order Differential Equations - Section 9.1 - Solutions, Slope Fields, and Euler's Method - Exercises 9.1 - Page 531: 7

$\dfrac{dy}{dx}=x-y$ and $y(1)=-1$

Take derivative of the given differential equation. $\dfrac{dy}{dx}=x-y(x)$ or, $\dfrac{dy}{dx}=x-y$ Now, apply the initial conditions, such as: $f(c)=-1 \implies \dfrac{dy}{dx}=x-y(x)$ Then, we have $y(1)=-1$