Does Dynare solve non-linear rational expectations models with expectations dated at t and at t-1?

example:

y(t) = aE(t)y(t+1)+bE(t-1)y(t)+c*x(t)+e(t)

Where y is the endogenous variable, x is exogenous, e is an error term and E(t-j)y(t+i) is the expectation based on the information at t-j of the variable y(t+i).

If so, how should I enter the term E(t-1)y(t)? Can I do it through a change of variable like

Sorry, for the delay in answering. In fact, Dynare can’t handle exactly that infinite sum over expectation set at an infinity of dates in the past. The only way I know of attacking the problem is to truncate the summation and express each term separately:
E(t-1)x(t)+E(t-2)x(t)+…+E(t-k)x(t)
if we only take into consideration the expectations formed over the k previous periods.

You can always check whether taking k+1 periods change a lot the results