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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Self-referential integration

Loading...

Similar Threads - Self referential integration | Date |
---|---|

A Lebesgue measure and integral | Jan 14, 2018 |

B Self learn calculus for UK A-levels? | Dec 15, 2017 |

B Names of elements of any equation | Jun 9, 2017 |

B What is the use of simplifying a question in math? | May 19, 2017 |

Looking for a insightful roadmap to learn math | Feb 28, 2015 |

**Physics Forums - The Fusion of Science and Community**