# In Problems 15–18 verify that the indicated function yexplicit solution of the given first-order differential equation. Pro-ceed as in Example 6, by considering o simply as a function and giveits domain. Then by considering o as a solution of the differentialequation, give at least one interval I of definition.30. In Exaу 3 фinterva15. (у — х)у' %—у — х+ 8; у%3Dх + 4Vx + 2is not a16. y' = 25 + y²; y= 5 tan 5xIn Problemsolution of17. y' = 2xy²; y = 1/(4 – x)%3D

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#17 help_outlineImage TranscriptioncloseIn 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 fullscreen
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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:

Step 2

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

Differentiation with r...

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MathCalculus

### Derivative 