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 (-00,-5) O (-10, -5] O (-10, 5) O [-5, 5] O (-5,00)
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 (-00,-5) O (-10, -5] O (-10, 5) O [-5, 5] O (-5,00)
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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Question
![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 (-00,-5)
O (-10, -5]
O (-10, 5)
O [-5, 5]
O (-5,00)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17677c9f-131d-467e-a7ce-1cf3bc92906c%2Fb4f22bec-b168-4efe-9870-882e92bc75fc%2F2awudx_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 (-00,-5)
O (-10, -5]
O (-10, 5)
O [-5, 5]
O (-5,00)
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