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Question 3 In this question, we consider the differential equation y" - 3y + 2y = f(x). (a) Suppose that in Eq. (2), f(x) = 0. (i) Write down the order and degree of the equation, then find two values of a so that ye is a solution of the equation. (ii) Write the differential equation as a system of first-order differential equations, then use the eigenvalue method to find the general solution of the system. (b) Suppose that in Eq. (2), f(x) = 4r. Use the method of undetermined coefficients to find a general solution for the equation. How many conditions are needed to find a particular solution for this equation?

Question 3 In this question, we consider the differential equation y" - 3y + 2y = f(x). (a) Suppose that in Eq. (2), f(x) = 0. (i) Write down the order and degree of the equation, then find two values of a so that ye is a solution of the equation. (ii) Write the differential equation as a system of first-order differential equations, then use the eigenvalue method to find the general solution of the system. (b) Suppose that in Eq. (2), f(x) = 4r. Use the method of undetermined coefficients to find a general solution for the equation. How many conditions are needed to find a particular solution for this equation?

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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Please answer first 3 questions which is (i), (ii) and (b)
Question 3 In this question, we consider the differential equation y"-3y + 2y = f(x). (a) Suppose that in Eq. (2), f(x) = 0. (i) Write down the order and degree of the equation, then find two values of a so that ye is a solution of the equation. (ii) Write the differential equation as a system of first-order differential equations, then use the eigenvalue method to find the general solution of the system. (b) Suppose that in Eq. (2), f(x) = 4r. Use the method of undetermined coefficients to find a general solution for the equation. How many conditions are needed to find a particular solution for this equation?
Transcribed Image Text:Question 3 In this question, we consider the differential equation y"-3y + 2y = f(x). (a) Suppose that in Eq. (2), f(x) = 0. (i) Write down the order and degree of the equation, then find two values of a so that ye is a solution of the equation. (ii) Write the differential equation as a system of first-order differential equations, then use the eigenvalue method to find the general solution of the system. (b) Suppose that in Eq. (2), f(x) = 4r. Use the method of undetermined coefficients to find a general solution for the equation. How many conditions are needed to find a particular solution for this equation?
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