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Save Determine whether the given function is a solution to the given differential equation. de e-2e"-3, + 40 = -6e 3t dt. The function @=2e - e is not a solution to the differential equation - de 0-+40 = -6e 3t because when 2 .4. 3t

Save Determine whether the given function is a solution to the given differential equation. de e-2e"-3, + 40 = -6e 3t dt. The function @=2e - e is not a solution to the differential equation - de 0-+40 = -6e 3t because when 2 .4. 3t

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Save Determine whether the given function is a solution to the given differential equation. de e=2e4-3t dr? 0- + 40 = -6 e 3t dt ..... The function 0 = 2 e 4t - e 3t is not a solution to the differential equation de + 40 = -6 e 3t, because when 2 e 4t - e 3t is substituted for 0, de -0- di? is substituted for and is substituted for the two sides of the differential equation dt dt are not equivalent on any intervals of t.
Transcribed Image Text:Save Determine whether the given function is a solution to the given differential equation. de e=2e4-3t dr? 0- + 40 = -6 e 3t dt ..... The function 0 = 2 e 4t - e 3t is not a solution to the differential equation de + 40 = -6 e 3t, because when 2 e 4t - e 3t is substituted for 0, de -0- di? is substituted for and is substituted for the two sides of the differential equation dt dt are not equivalent on any intervals of t.
Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 30x y' +2 (y')3 sin y- 10 (y')2 2 sin y+ 5xy - x° = 9, y'" = 6x° - 5y ..... 4 30x"y' +2 (y')3 sin y – 10 (y')² a solution to the differential equation. equivalent to y'' = Therefore, 2 sin y+ 5xy-x° = 9 which Applying implicit differentiation to the equation gives 6x -5y (Type an equation.)
Transcribed Image Text:Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 30x y' +2 (y')3 sin y- 10 (y')2 2 sin y+ 5xy - x° = 9, y'" = 6x° - 5y ..... 4 30x"y' +2 (y')3 sin y – 10 (y')² a solution to the differential equation. equivalent to y'' = Therefore, 2 sin y+ 5xy-x° = 9 which Applying implicit differentiation to the equation gives 6x -5y (Type an equation.)
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