A rabbit is trying to avoid detection by a nearby fox.

Initially, the fox and the rabbit are out of each other's sights as they are on opposite sides of a tree at the origin with the rabbit 1 unit North and the fox 1 unit South.

The fox starts to run directly to the left in a straight line with a constant speed 1 unit.

To avoid detection, the rabbit starts to run along a certain path with a constant speed 2 units, so as to always keep the tree between itself and the fox.

Find the differential equation which describes the path (in polar coordinates) of the hiding rabbit.