Look more carefully at the documentation on NDSolve. With NDSolve you get replacement rules which need to be used to access the solution. With NDSolveValue you get the solutions. The attached notebook gives both approaches. Also, it is best to not begin user variables with capitals since they can conflict with reserved names.

Kind regards,

David

Attachments:

Kepler's Derivation DK.nb

Mariusz,

I was writing my response while you posted yours. I like yours better. But why do we obtain different plots???

David

Ahh, my mistake was so simple, I should slap myself. Thank you, I spent a few hours looking over this thing trying to figure out my error just to simply find out (because of the .nb file that was provided) that instead of putting {X[t], Y[t]} I was putting {X,Y} so it was reading it incorrectly, again, thank you for your time! I appreciate it :3