Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y - x)y' = y = x + 2; y = x + 2√x+5 When y = x + 2√x + 5, y' = Thus, in terms of x, (y - x)y' = y-x+ 2 = Since the left and right hand sides of the differential equation are equal when x + 2√x+5 is substituted for y, y = x + 2√x + 5 is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. O (-10, 5) O (-5,00) O (-00,-5) O [-5, 5] O (-10, -5]
Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y - x)y' = y = x + 2; y = x + 2√x+5 When y = x + 2√x + 5, y' = Thus, in terms of x, (y - x)y' = y-x+ 2 = Since the left and right hand sides of the differential equation are equal when x + 2√x+5 is substituted for y, y = x + 2√x + 5 is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. O (-10, 5) O (-5,00) O (-00,-5) O [-5, 5] O (-10, -5]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8
![Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y = x + 2;
y = x + 2√x+5
When y = x + 2√x + 5,
y' =
Thus, in terms of x,
(y - x)y' =
y-x+ 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x+5 is substituted for y, y = x + 2√x + 5 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-10, 5)
O (-5,00)
O (-00,-5)
O [-5, 5]
O (-10, -5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F549955ac-feac-4a61-a87c-eadb5a4f2a1b%2F0c7e3260-c748-4369-8a7e-5d575a6079c0%2F3crwjxo_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y = x + 2;
y = x + 2√x+5
When y = x + 2√x + 5,
y' =
Thus, in terms of x,
(y - x)y' =
y-x+ 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x+5 is substituted for y, y = x + 2√x + 5 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-10, 5)
O (-5,00)
O (-00,-5)
O [-5, 5]
O (-10, -5]
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![Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y = x + 2;
y = x + 2√x+5
When y = x + 2√x + 5,
y' =
Thus, in terms of x,
(y - x)y' =
y-x+ 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x+5 is substituted for y, y = x + 2√x + 5 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-10, 5)
O (-5,00)
O (-00,-5)
O [-5, 5]
O (-10, -5]](https://content.bartleby.com/qna-images/question/549955ac-feac-4a61-a87c-eadb5a4f2a1b/aa3186fe-317b-4622-924c-4970da378807/lcf4wce_processed.png)
Transcribed Image Text:Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y = x + 2;
y = x + 2√x+5
When y = x + 2√x + 5,
y' =
Thus, in terms of x,
(y - x)y' =
y-x+ 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x+5 is substituted for y, y = x + 2√x + 5 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-10, 5)
O (-5,00)
O (-00,-5)
O [-5, 5]
O (-10, -5]
Solution
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