A non-holonomic solution in this case, roughly speaking, corresponds to a motion of the car by sliding in the plane.

When the right-hand side of the equation is a positive real number, the solution corresponds to an epispiral.

Most solutions to these conditions correspond to classes of surfaces, as in the following table:

The solution Godel found doesn't correspond to the universe we live in because we can show that the universe is not rotating.

One direct consequence is that two apparently different exact solutions could correspond to the same model universe, and differ only in their coordinates.

Conversely, any solution of the second equation corresponds to a solution to the first.

The three solutions presented by Bertrand correspond to different selection methods, and in the absence of further information there is no reason to prefer one over another.

Then the solution to the above example corresponds to:

The numerical solutions correspond to the underlined values.

The first solution corresponds to when the projectile is first launched.