Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation. 2y' = y³ cos(x); y = (1 - sin(x))-1/2 When y = (1 - sin(x))-1/2, 2y' = Thus, in terms of x, y³ cos(x) = Since the left and right hand sides of the differential equation are equal when (1-sin(x))-1/2 is substituted for y, y = (1 - sin(x))-1/2 is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. O ○ {x|× = 2n} ○ {x|× * = + 2nm} O {x|x # 2n} 0{x|x = =+20x} 0 {x|x = 7/} Then by considering as a solution of the differential equation, give at least one interval I of definition. (1/₁00) [플] O (5,5) [217,00) O O (277,00)
Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation. 2y' = y³ cos(x); y = (1 - sin(x))-1/2 When y = (1 - sin(x))-1/2, 2y' = Thus, in terms of x, y³ cos(x) = Since the left and right hand sides of the differential equation are equal when (1-sin(x))-1/2 is substituted for y, y = (1 - sin(x))-1/2 is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. O ○ {x|× = 2n} ○ {x|× * = + 2nm} O {x|x # 2n} 0{x|x = =+20x} 0 {x|x = 7/} Then by considering as a solution of the differential equation, give at least one interval I of definition. (1/₁00) [플] O (5,5) [217,00) O O (277,00)
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.
2y' = y³ cos(x); y = (1 - sin(x))-1/2
When y = (1 - sin(x))-1/2,
2y' =
Thus, in terms of x,
y³ cos(x) =
Since the left and right hand sides of the differential equation are equal when (1 - sin(x))-1/2 is substituted for y, y = (1 - sin(x))-1/2 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain.
O {x|x = 2nm}
0fx/x+2=}
O {x|x * 2n}
0{x|x==2m²}
0 {x|x *77}
Then by considering as a solution of the differential equation, give at least one interval I of definition.
(1/₁00)
[5]
(1,57)
[277, 00)
2π, 00)
O
O
O
O (2π, c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90812c35-7f3c-4fb7-8271-1d460ebe8990%2Fc8d07f8d-21b7-4952-b7b5-e929ee409fdc%2Fep2cb4e_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.
2y' = y³ cos(x); y = (1 - sin(x))-1/2
When y = (1 - sin(x))-1/2,
2y' =
Thus, in terms of x,
y³ cos(x) =
Since the left and right hand sides of the differential equation are equal when (1 - sin(x))-1/2 is substituted for y, y = (1 - sin(x))-1/2 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain.
O {x|x = 2nm}
0fx/x+2=}
O {x|x * 2n}
0{x|x==2m²}
0 {x|x *77}
Then by considering as a solution of the differential equation, give at least one interval I of definition.
(1/₁00)
[5]
(1,57)
[277, 00)
2π, 00)
O
O
O
O (2π, c
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