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Differential Equations

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Moderate

Existence and Uniqueness Moderate 1

DIFFEQ-XUO4CE

Consider the following differential equation:

$$x'=\frac{\sqrt{1-x^2}}{t-1}$$

For which of the following initial conditions is the equation guaranteed to have a unique solution that satisfies the initial condition?

Note: There may be multiple correct answers.

A

$x(0)=\cfrac{1}{2}$

B

$x(1)=\cfrac{1}{2}$

C

$x(-1)=-1$

D

$x(-1)=0$

E

$x(1/2)=0$

F

$x(0)=2$