Differential Equations Intro material

[dkotschessaa]

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

 

[manoj0071991]

1. e^kx
derivative is k.e^kx

 

[dkotschessaa]

Like I thought... too simple! Thanks!

-Dave K

 

[Bacle2]

How about also going from y'=ky

to y'/y= k, to

∫dy/y= ∫ k , etc.