Verify that the indicated function y = P(x) is an explicit solution of the given first-order differential equation. = 2xy; y = 1/(16 – x²) When y = 1/(16 – - x2), 2x y' = (16 – x²)² Thus, in terms of x, 2x 2xy? =| (16-²)²| 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 solution. Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.) y = 0(x)y= 0(x)is(-,-4)U(-4,4)U(4,00) Then by considering o as a solution of the differential equation, give at least one interval I of definition. (0, ∞) (-∞, -4] (-∞, 0) o (-4, 4) [4, 0)
Verify that the indicated function y = P(x) is an explicit solution of the given first-order differential equation. = 2xy; y = 1/(16 – x²) When y = 1/(16 – - x2), 2x y' = (16 – x²)² Thus, in terms of x, 2x 2xy? =| (16-²)²| 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 solution. Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.) y = 0(x)y= 0(x)is(-,-4)U(-4,4)U(4,00) Then by considering o as a solution of the differential equation, give at least one interval I of definition. (0, ∞) (-∞, -4] (-∞, 0) o (-4, 4) [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
Related questions
Question
![Verify that the indicated function y =
p(x) is an explicit solution of the given first-order differential equation.
y' = 2xy; y = 1/(16 – x
When y = 1/(16 – x²),
-
2x
y' =
(16 – x²)²
Thus, in terms of x,
2x
2xy2 =
(16 –x2)²
%3D
Since the left and right hand sides of the differential equation are equal when 1/(16 – x-) is substituted for y, y = 1/(16 –
- x3 is
solution.
Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.)
y =
P(x)y = q(x)is(-0,-4)U(-4,4)U(4,00) x
Then by considering o as a solution of the differential equation, give at least one interval I of definition.
(0, 0)
(-0, -4]
(-∞, 0)
o (-4, 4)
[4, 0)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20fa932-311a-46cd-86ab-78d74c804e39%2F61c1bf80-122a-49bc-8fd3-1386dd360262%2Fpwg7wjs_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' = 2xy; y = 1/(16 – x
When y = 1/(16 – x²),
-
2x
y' =
(16 – x²)²
Thus, in terms of x,
2x
2xy2 =
(16 –x2)²
%3D
Since the left and right hand sides of the differential equation are equal when 1/(16 – x-) is substituted for y, y = 1/(16 –
- x3 is
solution.
Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.)
y =
P(x)y = q(x)is(-0,-4)U(-4,4)U(4,00) x
Then by considering o as a solution of the differential equation, give at least one interval I of definition.
(0, 0)
(-0, -4]
(-∞, 0)
o (-4, 4)
[4, 0)
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