Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - Problems - Page 32: 7

$\frac{dy}{dx}=\frac{c-x}{y-c}$

Differentiate in respect to $x$, remembering to use chain rule. $$2(x-c)+2(y-c)\frac{dy}{dx}=0$$ Solve for the slope of the tangent line $\frac{dy}{dx}$ to get $$2(y-c)\frac{dy}{dx}=-2(x-c)$$ $$\frac{dy}{dx}=\frac{-(x-c)}{y-c}$$ $$\frac{dy}{dx}=\frac{c-x}{y-c}$$