Talk:Autonomous system (mathematics)

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Prime symbol polysemy[edit]

If I've understood this correctly, in Properties, y_0' means a value of the variable y which is not necessarily the same as y_0, whereas in Solution techniques: Second order, x' means the derivative of x. Would it be worth using distinct symbols, or at least adding some parenthetical disambiguation to Properties? Dependent Variable (talk) 22:09, 15 January 2011 (UTC)

Solution techniques[edit]

All of the solution techniques involve trying to get t = something, when the aim of solving something like \dot{x} = f(x) is to obtain a solution x(t), as t is the independent variable. Cases like x'' = f(x) cover huge areas of physics but the aim isn't to find out the time given f(x). In a few cases, like someone falling under gravity and experiencing atmospheric drag you end up finding an expression t = F(x) such that you can invert it to get x = F^{-1}(t), which is the solution. However, unless I'm missing something I don't see how saying the solution is to write the independent variable equal some (possibly horrible) expression is correct phrasing. — Preceding unsigned comment added by 193.35.132.25 (talk) 01:12, 10 July 2011 (UTC)