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Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" + 4y = 0 Oy"7y' +12y = 0 Oy"+ 2y + 2y = 0 Oy" + 2y + y = 0 Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁c₂ekz The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c₂ cos(x) + C₂ sin(x)). The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 2. The auxiliary equation should have a repeated negative root, so that the solution has the form c₂e-kx + c₂xe-kx O The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is t. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁*₁*

Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" + 4y = 0 Oy"7y' +12y = 0 Oy"+ 2y + 2y = 0 Oy" + 2y + y = 0 Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁c₂ekz The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c₂ cos(x) + C₂ sin(x)). The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 2. The auxiliary equation should have a repeated negative root, so that the solution has the form c₂e-kx + c₂xe-kx O The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is t. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁*₁*

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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Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" + 4y = 0 Oy"7y' +12y = 0 Oy"+ 2y + 2y = 0 Oy" + 2y + y = 0 Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁c₂ekz The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c₂ cos(x) + C₂ sin(x)). The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 2. The auxiliary equation should have a repeated negative root, so that the solution has the form c₂e-kx + c₂xe-kx O The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is t. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁*₁*
Transcribed Image Text:Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" + 4y = 0 Oy"7y' +12y = 0 Oy"+ 2y + 2y = 0 Oy" + 2y + y = 0 Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁c₂ekz The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c₂ cos(x) + C₂ sin(x)). The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 2. The auxiliary equation should have a repeated negative root, so that the solution has the form c₂e-kx + c₂xe-kx O The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is t. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁*₁*
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