Macroeconomic models are non-linear. The manual must explicitly show Taylor series approximations to convert structural equations into linear percentage deviations from the steady state.
After reviewing the solution, close the manual and re-derive the entire problem from scratch on your own. The true test of understanding is whether you can reproduce the correct results without looking. For an even deeper challenge, try to extend the model: How would the solution change if you altered a key assumption? This is precisely what the toughest end-of-chapter problems in Galí ask you to do.
