## 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