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+6 When y = x + 2√√√x + 6,
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+6 When y = x + 2√√√x + 6,
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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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+6
When y = x + 2√√x + 6,
1
y' = 1 +
√x+6
Thus, in terms of x,
(y-x)y' = 2√x+6+2
X
y-x+ 2 =
2√x+6+2
Since the left and right hand sides of the differential equation are equal when x + 2√x + 6 is substituted for y, y = x + 2√x + 6 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
x>-6
X
Then by considering as a solution of the differential equation, give at least one interval I of definition.
10 (-00,
-6)
O [-6, 6]
(-6,00)
O (-12, 6)
O (-12,
-6]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4203e2db-ceac-4178-99d9-66b64aca7b32%2F580f3fb8-fcb8-470e-816d-09df27bd522b%2Fvjnz33d_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+6
When y = x + 2√√x + 6,
1
y' = 1 +
√x+6
Thus, in terms of x,
(y-x)y' = 2√x+6+2
X
y-x+ 2 =
2√x+6+2
Since the left and right hand sides of the differential equation are equal when x + 2√x + 6 is substituted for y, y = x + 2√x + 6 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
x>-6
X
Then by considering as a solution of the differential equation, give at least one interval I of definition.
10 (-00,
-6)
O [-6, 6]
(-6,00)
O (-12, 6)
O (-12,
-6]
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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+6
When y = x + 2√√x + 6,
1
y= 1+ √==6
Thus, in terms of x,
(y - x)y' = 2x+6+2
X
y-x + 2 = |2x+6+2
X
Since the left and right hand sides of the differential equation are equal when x + 2√√x + 6 is substituted for y, y = x + 2√x + 6 is a solution.
Proceed as in Example 6, by considering & simply as a function and give its domain. (Enter your answer using interval notation.)
x < -6
X
Then by considering as a solution of the differential equation, give at least one interval I of definition.
0 (-00,
-6)
O [-6, 6]
Ⓒ (-6,0⁰)
O (-12, 6)
O (-12,
-6]](https://content.bartleby.com/qna-images/question/4203e2db-ceac-4178-99d9-66b64aca7b32/1714a545-4ca1-4757-9378-29b14402e57b/125coeqm_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+6
When y = x + 2√√x + 6,
1
y= 1+ √==6
Thus, in terms of x,
(y - x)y' = 2x+6+2
X
y-x + 2 = |2x+6+2
X
Since the left and right hand sides of the differential equation are equal when x + 2√√x + 6 is substituted for y, y = x + 2√x + 6 is a solution.
Proceed as in Example 6, by considering & simply as a function and give its domain. (Enter your answer using interval notation.)
x < -6
X
Then by considering as a solution of the differential equation, give at least one interval I of definition.
0 (-00,
-6)
O [-6, 6]
Ⓒ (-6,0⁰)
O (-12, 6)
O (-12,
-6]
Solution
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