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  • $\begingroup$ Hint: If you multiply by $r’(t)$, both terms will become the derivative of something. $\endgroup$
    – Ghoster
    Commented Apr 22, 2023 at 4:17
  • $\begingroup$ you can consider this is some kind of "homework asking" question, but to be honest, I have no idea how to solve differential equation, can you just give me the answer please ? $\endgroup$
    – Michael
    Commented Apr 22, 2023 at 4:19
  • 2
    $\begingroup$ Can you just give me the answer please? No, sorry, it would violate the policies of this site to provide a complete answer to a homework-like question like this. But I’m confused… if you don’t know anything about differential equations, why have you been assigned a problem that involves a differential equation? $\endgroup$
    – Ghoster
    Commented Apr 22, 2023 at 4:39
  • $\begingroup$ Maybe you would understand how to solve it using the conservation of energy instead of Newton’s Second Law. That still involves a differential equation, but one that involves only first-order derivatives. (It’s equivalent to the equation you’d get by following my hint.) $\endgroup$
    – Ghoster
    Commented Apr 22, 2023 at 4:45
  • $\begingroup$ Since this is a standard problem (often posed in terms of the Earth falling from rest into the Sun), you can certainly find solutions on the web, and probably in other questions on this site. $\endgroup$
    – Ghoster
    Commented Apr 22, 2023 at 4:49