- #1
dwilmer
- 11
- 0
How can you determine y's behavior from a direction field graph??
lets say i have the equation y' = 3 + 2y and i make a direction field graph.
I find equilibrium position at y = -3/2.
If question asks me to determine behavior of y as t approaches infinity, isn't this impossible, without solving the equation?
If i follow along the graph so that t is really big, then the graph still looks the same: a horizontal line at y = -3/2, where the slope of graph is zero. So how can i infer anything about y's behavior without first solving for y?
lets say i have the equation y' = 3 + 2y and i make a direction field graph.
I find equilibrium position at y = -3/2.
If question asks me to determine behavior of y as t approaches infinity, isn't this impossible, without solving the equation?
If i follow along the graph so that t is really big, then the graph still looks the same: a horizontal line at y = -3/2, where the slope of graph is zero. So how can i infer anything about y's behavior without first solving for y?