## For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to this equation t

Question

For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to this equation through the point

1. (−4,6)

2. (2,−6)

3. (−5,39)

4. (−1,45)

Please explain the process of obtaining the answer.

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2022-01-07T08:36:41+00:00
2022-01-07T08:36:41+00:00 1 Answer
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## Answers ( )

Answer:1. (-4,6) there is no a solution to the equation through this point

2. (2,−6) there is no a solution to the equation through this point

3. (−5,39) there is a solution to the equation through this point

4. (−1,45) there is a solution to the equation through this point

Step-by-step explanation:Using the existence and uniqueness theorem:

Let:

Now, let’s find the domain of , due to the square root:

So the domain of the function is:

Now, due to the fraction the denominator must be also different from 0, so:

So, the theorem tells us that for each there exists a unique solution defined in an open interval around .

1. (-4,6) there is no a solution to the equation through this point because

2. (2,−6) there is no a solution to the equation through this point because

3. (−5,39) there is a solution to the equation through this point because

4. (−1,45) there is a solution to the equation through this point because