In your opinion, does the equation linearize? How?

linearization.pdf (73.8 KB)

Every equation can be linearized if the involved functions are differentiable. Simply use a Taylor approximation. Without you providing context, it is impossible to tell where a complication might arise. It seems you have a problem with variances.

I did the part of linearization, right? And I have problems with linearization of sentences involving variance and exp , Can you help?

linearization.pdf (106 KB)

You still did not provide any context, just some math. Nobody knows what the variances are. Are they first or second order terms appearing in the equations, i.e. are the independent variables arising in the model, or are they the variances of other objects appearing in the model?

If I understand you correctly, you want to use the lognormal trick to approximate around a kind of stochastic steady state. That cannot be easily done in Dynare. Usually the proper way would be to enter the model in nonlinear form and then let Dynare do a higher order approximation.