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Consider the following second order differential equation y" - 4y + 8y = f(x) 1. Find the solution of the equation when f(x) = 0. 2. Find the form of a particular solution when f(x) = ² + cosx-re² sin 2r. 1 3. Find a particular solution when f(x)= sin 2x Question ?

Consider the following second order differential equation y" - 4y + 8y = f(x) 1. Find the solution of the equation when f(x) = 0. 2. Find the form of a particular solution when f(x) = ² + cosx-re² sin 2r. 1 3. Find a particular solution when f(x)= sin 2x Question ?

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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Question 1 Consider the following second order differential equation y" - 4y + 8y = f(x) 1. Find the solution of the equation when f(x) = 0. 2. Find the form of a particular solution when f(x) = ² + cosx-re² sin 2x. 1 3. Find a particular solution when f(x) = sin 2x Question 2 Find the recurrence Formula and the 6 first terms of the power series solution about zo = 0 of the initial value problem [(x²-1)" - xy + xy=0 [y(0) = 2, y'(0) = 1. Question 3 Consider the system X'(t) = AX(t) with A = 1. Find the eigenvalues and the eigenvectors of the matrix A. 2. Find a fundamental set of real valued solutions of the system.
Transcribed Image Text:Question 1 Consider the following second order differential equation y" - 4y + 8y = f(x) 1. Find the solution of the equation when f(x) = 0. 2. Find the form of a particular solution when f(x) = ² + cosx-re² sin 2x. 1 3. Find a particular solution when f(x) = sin 2x Question 2 Find the recurrence Formula and the 6 first terms of the power series solution about zo = 0 of the initial value problem [(x²-1)" - xy + xy=0 [y(0) = 2, y'(0) = 1. Question 3 Consider the system X'(t) = AX(t) with A = 1. Find the eigenvalues and the eigenvectors of the matrix A. 2. Find a fundamental set of real valued solutions of the system.
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