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Differential Equations

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Existence and Uniqueness in a Concrete Example 2

DIFFEQ-8GLPBN

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?

A

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

B

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

C

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

D

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