In this question, we consider the differential equation y" - 3y + 2y = f(x). (a) Suppose that in Eq. (2), f(x) = 0. (2) (i) Write down the order and degree of the equation, then find two values of a so that y = ea 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) = 4x. 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?
In this question, we consider the differential equation y" - 3y + 2y = f(x). (a) Suppose that in Eq. (2), f(x) = 0. (2) (i) Write down the order and degree of the equation, then find two values of a so that y = ea 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) = 4x. 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
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 help with A and B
Transcribed Image Text:In this question, we consider the differential equation
y" - 3y + 2y = f(x).
(a) Suppose that in Eq. (2), f(x) = 0.
(2)
(i) Write down the order and degree of the equation, then find two values of a so that
y = ez 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) = 4x. 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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