Mathematics

The slope of a solution curve at any point is simply the value of the derivative at that point. Since the differential equation $\frac{dy}{dx}=x^{2}-y$ directly tells you the slope in terms of $x$ and $y$, you don't need to solve the entire equation—just substitute the given coordinates into the right-hand side to read off the slope instantly.

The slope of a solution curve at any point is simply the value of the derivative at that point. Since the differential equation $\frac{dy}{dx}=x^{2}-y$ directly tells you the slope in terms of $x$ and $y$, you don't need to solve the entire equation—just substitute the given coordinates into the right-hand side to read off the slope instantly.