Key Sequence Notation New Concepts tying into Separated Equations: y’ = f(t,y) which are the most nicest. Recall that there was two special cases: seperable and autonomous ODEs. if we can write in terms of elementary function, good times if we can’t do it in terms of elementary functions, we can use qualitative analysis t(slope field, etc.) recall again Newton’s Law of Cooling phase line and stability (ODEs) Important Results / Claims autonomous First Order ODEs’ solutions do not cross; as in, if there are two solutinos y_1 and y_2, their curves never intersect. one and exactly one solution exist for every point of an IVP autonomous ODEs level off at stationary curves Questions Interesting Factoids