Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - True-False Review - Page 32: f

True

An isocline is in the form $f(x,y)=k$ Given: $\frac{dy}{dx}=\frac{x^2+y^2}{2y}\\ \rightarrow 2ky=x^2+y^2$ If we set the equation $x^2+(y-k)^2-k^2$ to $0$, we have: $x^2+(y^2-2yk+k^2)-k^2=0\\ \Leftrightarrow x^2+y^2=2yk$ Since the equation is equal to the slope, hence, the statement is true.