## MIT 1803 lecture 5

This lecture started with noting that equations of the form $y' = f(y)$ where there is no dependence in the RHS on $t$ are known as autonomous, and can be dealt by separation of variables (so I realized that I use separation of variables all the time without realizing it, in these simpler dy/dx formulas.)

Critical points are $y_0$ s.t. $f(y_0) = 0$ , creating bounding integral curves.

The logistic equation $y'=ky$ where $k=a-by$ and demonstrated critical points which are when $y'=0$ and what they can tell you.  Plot the y’ vs y and y vs. t for quick intuition about what the system is doing.