How can l prove that Newton's laws are time invariant?

[stefano77]

how can l prove Newton's law is time invariant?

if x (t) is a solution of dd/ddx x(t) = f(x(t)) then if l put y(-t) dd/ddt y(t)=dd/ddt x(-t). Now how dd/ddt x(-t) is equal to f(x(-t))?dd/ddt is second derivative with respect to time

 

[Ibix]

You've previously used LaTeX on this site. Can I suggest you repost the above using LaTeX? If you have forgotten the syntax there is a guide linked below the reply box. If the LaTeX does not render when you try to preview it, refresh the page while in preview and it should work (you may wish to copy your text to clipboard first as a safety measure).

 

[topsquark]

how can l prove Newton's law is time invariant?

if x (t) is a solution of dd/ddx x(t) = f(x(t)) then if l put y(-t) such that dd/ddt y(t)=dd/ddt x(-t). Now how dd/ddt x(-t) is equal to f(x(-t))?dd/ddt is second derivative with respect to time

$\dfrac{d^2}{dt^2} y(-t) = \dfrac{d^2}{dt^2} x(t)$

or equivalently
$\dfrac{d^2}{d(-t)^2} y(t) = \dfrac{d^2}{d(-t)^2} x(-t)$

Can you finish?

-Dan

Addendum: Please note my addition of "such that" to your original post. You needed something to separate those two expressions.