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Asked Jan 25, 2020
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#17

In Problems 15–18 verify that the indicated function y
explicit solution of the given first-order differential equation. Pro-
ceed as in Example 6, by considering o simply as a function and give
its domain. Then by considering o as a solution of the differential
equation, give at least one interval I of definition.
30. In Exa
у 3 ф
interva
15. (у — х)у' %—у — х+ 8; у%3Dх + 4Vx + 2
is not a
16. y' = 25 + y²; y= 5 tan 5x
In Problem
solution of
17. y' = 2xy²; y = 1/(4 – x)
%3D
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In Problems 15–18 verify that the indicated function y explicit solution of the given first-order differential equation. Pro- ceed as in Example 6, by considering o simply as a function and give its domain. Then by considering o as a solution of the differential equation, give at least one interval I of definition. 30. In Exa у 3 ф interva 15. (у — х)у' %—у — х+ 8; у%3Dх + 4Vx + 2 is not a 16. y' = 25 + y²; y= 5 tan 5x In Problem solution of 17. y' = 2xy²; y = 1/(4 – x) %3D

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Step 1

First find the domain of the function y = 1 / (4 - x2)

 

The zeros of the denominator are (4 - x2) = 0 or x = 2, -2

 

The function y = 1 / (4 - x2), the domain of the function is set of all real numbers excluding 2, -2.  

 

Therefore, the domain of the function y = 1 / (4 - x2) is:

Calculus homework question answer, step 1, image 1
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Step 2

Now consider y = 1 / (4 - x2) as a function of x.

 

Differentiation with r...

Calculus homework question answer, step 2, image 1
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Derivative

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