Let \(f:\RR\to\RR\) be bounded and continuously differentiable. Show that every solution \(y\) of \[ y'=f(y) \] is monotone.
Solutions of autonomous ODEs $y'=f(y)$ are monotone
P-BKS19-2A
- Area
- Prelim
- Seen at
- BERKELEY
- Years
- 2019
- Status
- draft
P-BKS19-2A
Let \(f:\RR\to\RR\) be bounded and continuously differentiable. Show that every solution \(y\) of \[ y'=f(y) \] is monotone.