Trouble with the constant when finding a function $x(t)$ such that $\dot{x}(t) = x(t)^2t$

I'm attempting to consider a function $x(t)$ such that $$\dot{x}(t) = x(t)^2t.$$ I exercised for my self that it has something to do with the $x(t) = -2t^{-2}$ yet I could not exercise just how to place the constant in to make sure that the function still functioned.

Ever since I've been informed that the function is $x(t) = \frac{2}{c-t^2}$ and also I can conveniently see that this function works yet I can not exercise just how to get to that solution without simply needing to detect it. Exists a means to function this out or does one simply require to be efficient detecting these points?

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2022-07-25 20:45:12
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