Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y-x)y' = y - x + 18; y = x + 6√x +3 When y = x + 6√√x + 3, y' = Thus, in terms of x, (y - x)y' = y-x + 18 = Since the left and right hand sides of the differential equation are equal when x + 6√x + 3 is substituted for y, y = x + 6√x + 3 is a solution. Proceed as in Example 6, by considering p simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering p as a solution of the differential equation, give at least one interval I of definition. O (-3,00) O (-6, -3] O(-6, 3) O (-00, -3) O [-3, 3]
Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y-x)y' = y - x + 18; y = x + 6√x +3 When y = x + 6√√x + 3, y' = Thus, in terms of x, (y - x)y' = y-x + 18 = Since the left and right hand sides of the differential equation are equal when x + 6√x + 3 is substituted for y, y = x + 6√x + 3 is a solution. Proceed as in Example 6, by considering p simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering p as a solution of the differential equation, give at least one interval I of definition. O (-3,00) O (-6, -3] O(-6, 3) O (-00, -3) O [-3, 3]
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 + 18;
y=x+6√x + 3
When y = x + 6√x + 3,
y' =
Thus, in terms of x,
(y - x)y' =
y-x + 18 =
Since the left and right hand sides of the differential equation are equal when x + 6√x + 3 is substituted for y, y = x + 6√x + 3 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 (-3,00)
O(-6, -3]
O (-6, 3)
O (-00, -3)
O [-3, 3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb66b754d-124e-412b-a333-c35d8253d007%2F64b70286-ff26-446f-bcc0-8751709ebb55%2Fxpla46i_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 + 18;
y=x+6√x + 3
When y = x + 6√x + 3,
y' =
Thus, in terms of x,
(y - x)y' =
y-x + 18 =
Since the left and right hand sides of the differential equation are equal when x + 6√x + 3 is substituted for y, y = x + 6√x + 3 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 (-3,00)
O(-6, -3]
O (-6, 3)
O (-00, -3)
O [-3, 3]
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