# Talk:Autonomous system (mathematics)

WikiProject Mathematics (Rated Start-class, Mid-importance)
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Field: Mathematical physics
WikiProject Physics (Rated Start-class, Low-importance)
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WikiProject Systems (Rated Start-class, Mid-importance)
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)