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3. In the following questions, each part is independent. (a). Suppose that a 5-th order homogeneous linear differential equation with constant woefficients has characteristic roots li.e., the corresponding characteristic polynomial has the roots). - 2-3i, -2+3i, 5, 5 and -1. Find a general solution to this differential equation. x-2 are solutions to (b). Show that x² and x-² are x²y" + xy² - 4y = 0, where x >0 Find a general solution of this differential equation. reason why your solution is a general solution. Give a

3. In the following questions, each part is independent. (a). Suppose that a 5-th order homogeneous linear differential equation with constant woefficients has characteristic roots li.e., the corresponding characteristic polynomial has the roots). - 2-3i, -2+3i, 5, 5 and -1. Find a general solution to this differential equation. x-2 are solutions to (b). Show that x² and x-² are x²y" + xy² - 4y = 0, where x >0 Find a general solution of this differential equation. reason why your solution is a general solution. Give a

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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3. In the following questions, each part is independent. (a). Suppose that a 5-th order homogeneous linear differential equation with constant wefficients has characteristic roots li.e., the corresponding characteristic polynomial has the roots). - 2-3i, −2+3i, 5, 5 and -1. Find a general solution to this differential equation. (b). Show that x² and x-² are solutions to x²y" + xy² - 4y = 0, where x>0 Find a general solution of this differential equation. reason why your solution is a general solution. Give a
Transcribed Image Text:3. In the following questions, each part is independent. (a). Suppose that a 5-th order homogeneous linear differential equation with constant wefficients has characteristic roots li.e., the corresponding characteristic polynomial has the roots). - 2-3i, −2+3i, 5, 5 and -1. Find a general solution to this differential equation. (b). Show that x² and x-² are solutions to x²y" + xy² - 4y = 0, where x>0 Find a general solution of this differential equation. reason why your solution is a general solution. Give a
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Step 1: write the given roots

open parentheses a close parentheses Suppose space that space the space 5 to the power of th space order space homogeneous space linear space differential space equation space with space constant space coefficient space has space characteristic space roots space are space minus 2 minus 3 straight i space comma space minus 2 plus 3 straight i space space comma space 5 space 5 space comma negative 1

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