So of course the first thing I did was integrated it a few times to get:Show that a curve such that everywhere is contained in a plane

where the a, b and c's are constants.

Now how do I continue from there?

EDIT:

Actually I think I have it,

The parametric equation of a plane is

where t and u are the varying parameters. In the above integrated equation, there's 2 varying parameters, and so it almost fits the equation of a plane, but in this case u is restricted to u=t^2