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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
See en.wikipedia.org/wiki/… –  Ayman Hourieh Dec 2 '12 at 15:46
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2 Answers

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.

I think there are many examples of this type of ODE in real life; to name a few 1) rate of change of a population (must be related to current population) 2) radioactive decay of an element (related to how much of the element currently remains) 3) compound interest (related to how much money we originally started with)

see what else you can come up with.

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The keyphrases are $$\rm exponential\ growth$$ and $$\rm exponential\ decay$$ Type these into the internet and watch the applications flood in.

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