Suppose that we have a function that refers to itself in its derivative or second derivitive.(adsbygoogle = window.adsbygoogle || []).push({});

For example, let's say that you have a spring for which the force is directly proportional to the distance the spring has been compressed.

F = -cx

For simplicity's sake, mass is constant, so we can just say

a = -cx

The differential-form equation for this acceleration is:

d^{2}x/(dt)^{2}= -cx

And so the speed equation is

dx/dt = v_{0}+ [inte]-cx(dt)

How would you solve this?

Or, for a simpler equation, say that the velocity of a particle depends on its position:

dx/dt = c_{1}+ c_{2}x

How would you solve this to get to the position function?

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# Self-referential integration

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