Evaluating a differential equation

Suppose I have y = const/r^2, r = r(t)

Then if @ = partial derivative and dr/dt = v, I can say:

dy/dt = @y/@dr dr/dt + @y/@dt dt/dt = - 2 const v(t) /r^3 (1)

The solution is obviously y = const/r(t)^2, but what methods could I
have used to solve (1) ?

Thankyou

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