Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. y' = 2xy²; y = 1/(16-x²) When y = 1/(16 - x²), y' = Thus, in terms of x, 2xy2 = Since the left and right hand sides of the differential equation are equal when 1/(16-x2) is substituted for y, y = 1/(16-x2) 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. 0 (-00, 0) O [4,00) O (-4,4) (0,00) O (-00, -4]
Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. y' = 2xy²; y = 1/(16-x²) When y = 1/(16 - x²), y' = Thus, in terms of x, 2xy2 = Since the left and right hand sides of the differential equation are equal when 1/(16-x2) is substituted for y, y = 1/(16-x2) 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. 0 (-00, 0) O [4,00) O (-4,4) (0,00) O (-00, -4]
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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9
![Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
y' = 2xy²; y = 1/(16 - x²)
When y= 1/(16 - x²),
y' =
Thus, in terms of x,
2xy² =
Since the left and right hand sides of the differential equation are equal when 1/(16-x2) is substituted for y, y = 1/(16-x2) 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.
0 (-00, 0)
O [4,00)
(-4,4)
0 (0,00)
O (-∞, -4]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F549955ac-feac-4a61-a87c-eadb5a4f2a1b%2F52e77c1c-e482-4123-97dc-e4b28bd722cd%2F5aqibka_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' = 2xy²; y = 1/(16 - x²)
When y= 1/(16 - x²),
y' =
Thus, in terms of x,
2xy² =
Since the left and right hand sides of the differential equation are equal when 1/(16-x2) is substituted for y, y = 1/(16-x2) 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.
0 (-00, 0)
O [4,00)
(-4,4)
0 (0,00)
O (-∞, -4]
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