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Verify that the indicated function y = g(x) is an explicit solution of the given first-order differential equation. y' = 2xy2; y = 1/(16 – x2) When y = 1/(16 – x²), 2x y' = (16 – 2)2 Thus, in terms of x, 2x 2xy2 : (16 – x²)² | 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 simply as a function and give its domain. (Enter your answer using interval notation.) y=0(x)y= ) = »(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) • (-4, 4) [4, 0)

Verify that the indicated function y = g(x) is an explicit solution of the given first-order differential equation. y' = 2xy2; y = 1/(16 – x2) When y = 1/(16 – x²), 2x y' = (16 – 2)2 Thus, in terms of x, 2x 2xy2 : (16 – x²)² | 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 simply as a function and give its domain. (Enter your answer using interval notation.) y=0(x)y= ) = »(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) • (-4, 4) [4, 0)

Advanced Engineering Mathematics
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 = e(x) is an explicit solution of the given first-order differential equation. y' = 2xy2; - x²) y = 1/(16 – When y = 1/(16 – x2), - 2x y' = (16 – x²)² Thus, in terms of x, 2х 2xy? = (16 –2?)? Since the left and right hand sides of the differential equation are equal when 1/(16 – x) is substituted for y, - y = 1/(16 – x²) 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.) y = 0(x)y = 0(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)
Transcribed Image Text:Verify that the indicated function y = e(x) is an explicit solution of the given first-order differential equation. y' = 2xy2; - x²) y = 1/(16 – When y = 1/(16 – x2), - 2x y' = (16 – x²)² Thus, in terms of x, 2х 2xy? = (16 –2?)? Since the left and right hand sides of the differential equation are equal when 1/(16 – x) is substituted for y, - y = 1/(16 – x²) 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.) y = 0(x)y = 0(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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