One standard example when introducing OLS in econometric classes is modelling the log-wage by education and experience. Often, the example models account for experience by not only by the experience itself but additionally but the squared experience. This is done because a non-linear relationship is assumed. This yields the theoretical model
$E[\log(Y)|X] = \beta_0 + \beta_1Education + \beta_2Experience + \beta_3Experience^2$.
However, one assumption in OLS is that the dependent variable is linear in all its components. How can then this serve as an example when apparently some nonlinear relationship is existing?
What confuses me is that even though the squared experience and log-wage may have a linear relationship, there is still the original variable in the model which has apparently a nonlinear relationship with log-wage. So, in this case it's linear in Education and squared Experience but it's still nonlinear in Experience itself.