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!)

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# Algebraic Equation

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