# Need to explain an application of $y' = ky$

I have to write application of the ODE $y' = ky$. i want application or any that explain little bit. Thanks!

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Random capitalization Makes titles look Rather foolish. –  Chris Eagle Dec 2 '12 at 15:11
its better to give answer then finding problems. –  Krunal Dec 2 '12 at 15:18
@Krunal: In this case, we first find the problems and then give an answer. Or isn't that what you intended to say? –  akkkk Dec 2 '12 at 15:23
–  Ayman Hourieh Dec 2 '12 at 15:46

This is an ODE which says that the rate of change ($y'$) of $y$ is equal to some constant $k$ times $y$; the solutions of which are the class of exponential functions.
The keyphrases are $$\rm exponential\ growth$$ and $$\rm exponential\ decay$$ Type these into the internet and watch the applications flood in.