Is it correct to linearize a part of a differential equaztion?

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if I'm not wrong, if I have a differential equation like this:

$Dl=a_0k_1 + k_1a_1x + k_1a_2x^2 - k_1l$

and I want to linearize it, I can linearize only the quadratic part (ergo, $k_1a_2x^2$ ). Right?

But then, when I carry out the linearization around $x_0=0$ of that part, I will end up with:

$Dl=a_0k_1 + k_1a_1x + 2k_1a_2x - k_1l$

Am I right? What Am I doing wrong?

Thank you very much!