Nonstationarity Panel Data

I'm working with a panel dataset and unit root tests suggest that my dependent variable in nonstationary. I know that I can take first differences to try to deal this issue. When I do, my results are much different than those under a FE specification. I wonder whether this is due to my variables being nonstationary or to the information loss that first differencing entails. I don't know which results to trust.

Are there are other methods to make series stationary? If so, I'd like to explore those options. In particular, does using a dynamic approach resolve the nonstationarity issue? I can't seem to find a clear answer to this question.