I feel this pain Mine doesn’t understand that incomplete worksheets aren’t lecture notes and his handwriting is worse than any doctor’s I encountered in 10 years of pharmacist practice before going into engineering
Thank you my friend. Currently studying to enter into grad school for Quantitative Bio. The journey has been challenging but it is people like you who make the challenge seem surmountable... and loads of fun! Please make others! Perhaps SIR model of disease transmission, Levins meta-population model, Tillman's model of resource competition, or Holling's disc equation. Best wishes fellow nerds!
That is the case here, but it can't be guaranteed in general. Because we have linearised the system, we're ignoring any higher order terms. Have a look at what happens in the example dx/dt = y, dy/dt = y^3 - x.