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Differential Equations Intro material

  • #1
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Homework Statement



What function do you know from calculus is such that its first derivative is a constant multiple k of itself? (Do not use the function f(x) = 0.)



Homework Equations



The previous question asked what function was a derivative of itself - with the pretty easy answer of e^x. But I'm stuck on this one.


The Attempt at a Solution



To figure it out would involve finding the solution to something like:

y' = ky

Or at least that's the answer to the follow up question, which asks what differential equation this would satisfy. So it's something I just need to know.

I think I'm missing something very simple. I looked through all my calculus material and am at a loss to find such a function, though I have a feeling it's easier than I'm making it.

-Dave K
 

Answers and Replies

  • #2
1. ekx
derivative is k.ekx
 
  • #3
1,047
775
Like I thought... too simple! Thanks!

-Dave K
 
  • #4
Bacle2
Science Advisor
1,089
10
How about also going from y'=ky

to y'/y= k, to

∫dy/y= ∫ k , etc.
 

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