After trying several models with my data, R^2 and p values are showing my model looks like below. ACF plot tells me AR term is significant. Insights into data tells me change in 'x' would have impact(say y is A/C usage and x is temperature).

```
  y(t)=a+b*y(t-1)+c*{x(t)-x(t-1)}+error

```

Question: Is the above model statistically meaningful? If so, what is the category of this "linear model" called? I came across AR models, MA models and ARIMA/ARMA models, but havent seen a model where AR term and diff(independent variable) exists together.