Verify that the indicated function y = 4(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 – x) is substituted for y, y = 1/(16 – x<) 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 o as a solution of the differential equation, give at least one interval I of definition. (0, ∞) O (-0, -4] o (-∞, 0) o (-4, 4) O [4, 0)
Verify that the indicated function y = 4(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 – x) is substituted for y, y = 1/(16 – x<) 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 o as a solution of the differential equation, give at least one interval I of definition. (0, ∞) O (-0, -4] o (-∞, 0) o (-4, 4) O [4, 0)
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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![Verify that the indicated function y = 4(x) is an explicit solution of the given first-order differential equation.
= 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 – x) is substituted for y,
-
y = 1/(16 – x<) 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 o as a solution of the differential equation, give at least one interval I of definition.
(0, ∞)
O (-0, -4]
o (-∞, 0)
o (-4, 4)
O [4, 0)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6698ae8-6c01-4434-828e-21af6fc513df%2F3ed489f1-8524-4476-9c1b-91af52b75fe4%2Fpg4me4p_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that the indicated function y = 4(x) is an explicit solution of the given first-order differential equation.
= 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 – x) is substituted for y,
-
y = 1/(16 – x<) 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 o as a solution of the differential equation, give at least one interval I of definition.
(0, ∞)
O (-0, -4]
o (-∞, 0)
o (-4, 4)
O [4, 0)
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