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Consider the first order differential equation:

$$\begin{equation} \frac{dy}{dt} = \frac{t}{y}, y(0) = 1 \end{equation}$$

Which of the following statements is true?

There is a some interval $|t|exists a unique solution.

There is no guarantee of a unique solution passingthrough $(t=0,y=1)$

There do not exist any solutions passing through$(t=0,y=1)$

There are infinitely many solutions passing through$(t=0,y=1)$