Verify that the indicated function y p(x) is an explicit solution of the given first-order differential equation. y = x + 2√x + 5 (y - x)y' = y - x + 2; When y = x + 2√x + 5, 1 y' = 1 + √x+5 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 o 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) Ⓒ (-5,00) O (-10, -5] O [-5, 5]
Verify that the indicated function y p(x) is an explicit solution of the given first-order differential equation. y = x + 2√x + 5 (y - x)y' = y - x + 2; When y = x + 2√x + 5, 1 y' = 1 + √x+5 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 o 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) Ⓒ (-5,00) O (-10, -5] O [-5, 5]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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,
1
y' = 1 +
√x + 5
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 o 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)
Ⓒ (-5,00)
O (-10, -5]
O [-5, 5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa28615ab-e033-4f44-8440-73dc9a67f4dd%2Fbd7477ed-c64d-44af-bd5c-61af4aa51a49%2Frkokis_processed.jpeg&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,
1
y' = 1 +
√x + 5
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 o 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)
Ⓒ (-5,00)
O (-10, -5]
O [-5, 5]
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