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## Homework Statement

Hi all

I have the following expression

[tex]

\frac{dy}{dt}= \sqrt{C-y(t)^2},

[/tex]

where C is a constant, and y is the variable, which depends on t. What I need to do is to solve this differential equation, but my problem is that this is a math-class (and not a physics-class), so I need to be very rigorous.

Now it is almost mandatory to comment of the argument of a squareroot. What I know is that the solution

*y*is real.

Thus the term C-y(t) cannot be less than zero. But my

**question**is: Does it make sense to talk about the term "C-y(t)" being less than zero, when y(t) is time-dependent?

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