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Find the general solution of each of the following homogeneous equations. Use the method of reduction of order to find your second solution. State your final answer in terms of as few abritrary constants as possible. 1 (a) x²y" + 3xy' + y = 0 (where x > 0), given solution yı (b) x²y" - 2xy' + (x²+2)y = 0, given solution y₁ = x sin x

Find the general solution of each of the following homogeneous equations. Use the method of reduction of order to find your second solution. State your final answer in terms of as few abritrary constants as possible. 1 (a) x²y" + 3xy' + y = 0 (where x > 0), given solution yı (b) x²y" - 2xy' + (x²+2)y = 0, given solution y₁ = x sin x

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 6CT
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2. Find the general solution of each of the following homogeneous equations. Use the method of reduction of order to find your second solution. State your final answer in terms of as few abritrary constants as possible. (a) x²y" + 3xy' + y 0 (where x > 0), given solution yı = (b) x²y" - 2xy + (x²+2)y = 0, given solution y₁ = x sin x = 1 - X
Transcribed Image Text:2. Find the general solution of each of the following homogeneous equations. Use the method of reduction of order to find your second solution. State your final answer in terms of as few abritrary constants as possible. (a) x²y" + 3xy' + y 0 (where x > 0), given solution yı = (b) x²y" - 2xy + (x²+2)y = 0, given solution y₁ = x sin x = 1 - X
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