$$y_{t+2}-2y_{t+1}+y_t=-15$$ Getting $y^{h}_t$ is fairly simple, and I get $$(C_1+C_2)1^t$$ However, getting $y^{p}_t$ is a bit harder, and requires "guessing" as our professor says. I have been "guessing" for $$y^{p}_t=A$$ $$y^{p}_t=At$$ However, the solution is supposedly $$y^{p}_t=At^2$$ $$y^{p}_{t+1}=A(t+1)^2$$ $$y^{p}_{t+2}=A(t+2)^2$$
But can anyone tell me how $$At^2$$ turns into $$A(t+2)^2$$
Thanks!