Linearization of nonlinear state equation around working points

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I'm confused about equilibrium points and operating points, are they two different things or the same thing?

How would one (or what are the steps to) solve the following equation if operating points are given: $x_{10}=1$ , $x_{20}=2$? $$$$

$\dot{x_1}=e^{x_1}-x_2+u$

$\dot{x_2}=2x_1-x_2$

$y=x_1^2+x_2^2$