# Implicit Linear multistep method order?

Considering the following linear multistep method:

$$y_{k+2} = y_{k+1} + \frac{h}{12} \left( -f(x_{k},y_{k}) + 8f(x_{k+1},y_{k+1})+ 5f(x_{k+2},y_{k+2}) \right)$$

What is it's order? What is the maximum order that this method can attain?

To determine an upper bound for the order, insert $$f(x,y)=y$$ and $$y_k=e^{kh}$$ and compute the difference of both sides. $$e^{2h}-e^h-\frac{h}{12}(-1+8e^h+5e^{2h})$$ and then insert the Taylor series of the exponential.