I have the following problem.
If we express the curve of the cycloid in the form of a function $y=ϕ(x)$, show if it is possible to eliminate parameter $t$ in order to determine the cartesian representation of the cycloid.
Show that function $y=ϕ(x)$ satisfies the differential equation
$$(1 + (y')²) y = 2a$$
I know that the parametric equations for the cycloid are:
$$x=r(t—\sin(t)),\quad y=r(1—\cos(t))$$
I really do not know what is a $y=ϕ(x)$ function, or how can use that function to solve the rest of the problem
Could you please show me what is this function, give me an example on how to solve this, or maybe give me a link to a website where I can learn about this.
Please excuse my English. Thanks.