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## Homework Statement

Is ##f(t,y)=e^{-t}y## Lipschitz continuous in ##y##

## Homework Equations

I don't really know what to put here. Here is the definitions:

https://en.wikipedia.org/wiki/Lipschitz_continuity

## The Attempt at a Solution

I have found out that I can determine whether a function is Lipschitz continuous by looking at it's derivative ##f_y = df/dy## and see if it is bounded. In my case ##f_y=e^{-t}## is bounded in ##(y,f_y)## plane but is NOT bounded in ##(t,f_y)## plane. My conclusion is that ##f(t,y)## Lipschitz continuous in ##y##, right? I don't see why it should matter if ##f_y## is not bounded in ##(t,f_y)## plane. Is statement correct?