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On the exam I was asked the question about Transcritical bifurcation. I gave the equation

$$ \dot x = rx - x^2 $$

Then I was asked why it is not a differential equation and I couldn't answer. I thought if some derivative equals a function - it is a differential equation.

It's not a differential equation, because r is a variable not x?*

*Sorry If something is not clear. I suffer for lack of math in english.

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    Why not? If $r$ is a parameter, this is a differential equation.2012-03-05
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    Not sure but in bifurcation analysis r is a variable.2012-03-05
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    It is not linear differential equation but it is a differential equation because of x'.2012-03-05

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