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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/(16x2) is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) 4 Then by considering op as a solution of the differential equation, give at least one interval I of definition. 0 (-∞, 0) O (-4,4) 0 (0,00) O [4,00) O -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/(16x2) is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) 4 Then by considering op as a solution of the differential equation, give at least one interval I of definition. 0 (-∞, 0) O (-4,4) 0 (0,00) O [4,00) O -4]

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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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. O (-∞, 0) O (-4,4) O (0, ∞) O [4, ∞) (-∞, -4]
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. O (-∞, 0) O (-4,4) O (0, ∞) O [4, ∞) (-∞, -4]
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