Pair of differrential equations that describes motion of planet about sun using first two laws of Kepler is given as:

$$2 \dot{r}\dot{\theta} + r \ddot{\theta} = 0$$ and $$\ddot{r} + r\dot{\theta}^2 \left(r \frac{a}{b^2} - 1\right) = 0$$

$$2 \dot{r}\dot{\theta} + r \ddot{\theta} = 0$$ and $$\ddot{r} + r\dot{\theta}^2 \left(r \frac{a}{b^2} + 1\right) = 0$$

$$2 \dot{r}\dot{\theta} - r \ddot{\theta} = 0$$ and $$\ddot{r} - r\dot{\theta}^2 \left(r \frac{a}{b^2} - 1\right) = 0$$

$$2 \dot{r}\dot{\theta} - r \ddot{\theta} = 0$$ and $$\ddot{r} - r\dot{\theta}^2 \left(r \frac{a}{b^2} + 1\right) = 0$$