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  • $\begingroup$ Why do you expect different values of y to give the same value for x? You need to change C for that to be true. $\endgroup$
    – Boba Fit
    Commented Jan 3, 2023 at 13:34
  • 1
    $\begingroup$ You got x and y mixed up, but anyways as you can see in the picture above, points for which y is the same and x is different exist. And if I have understood correctly, C is a constant that I cannot change for different points $\endgroup$ Commented Jan 3, 2023 at 13:55
  • $\begingroup$ Related : What is the position as a function of time for a mass falling down a cycloid curve?. $\endgroup$
    – Frobenius
    Commented Jan 3, 2023 at 14:38