I have a question regarding my introductory differential equations course. I'm lost regarding this question:
"Consider the following Initial Value Problem: $dy/dt = f(y)$, with initial condition $y(0) = y_0$, where $f(y)$ and $f'(y)$ are continuous for all $y$ (implies a unique solution). Suppose that $f(y_0) \neq 0$ (cannot equal $0$). Then it can be shown that the solution to the above Initial Value Problem is monotonic (strictly increasing or decreasing). Provide a careful argument that justifies this claim, based on sketches of integral curves."
Any ideas on how to go about this? I'm not quite sure what $f(y_0)$ represents or if the variable $t$ is involved (if it isn't obvious by now it's my first DE course). Any help/guidance on this question would be greatly appreciated. Thanks everyone