I read in my notes that if you have an(adsbygoogle = window.adsbygoogle || []).push({}); algebraic equationof the form:

[tex]0=f(\dot{z},z,u,t)[/tex]

And you find an equilibrium solution, [tex]\dot{z}\equiv 0 [/tex]

Then there exists (J) a function: [tex] z= f(u)[/tex]

Is this always true of an algebraic equation?

An algebraic equation being defined as:

http://mathworld.wolfram.com/AlgebraicEquation.html

If this is true, could someone show me the proof? (Hopefully its not a big nightmare!)

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Algebraic Equation

**Physics Forums | Science Articles, Homework Help, Discussion**