Explanation Procedure used: General solution of a higher order differential equation. In order, to solve an n th order differential equation a n y n + a n − 1 y n − 1 + ... a 2 y ″ + a 1 ′ + a 0 y = 0 , initially solve the n th degree polynomial equation a n m n + a n − 1 m n − 1 + ...... + a 0 = 0 . If all the roots of a n m n + a n − 1 m n − 1 + ...... + a 0 = 0 are real and distinct, then the general solution will be y = c 1 e m 1 x + c 2 e m 2 x + ⋯ + c n e m n x . If an auxiliary equation has k roots and all the roots of the auxiliary equation are equal, then the general solution will be y = c 1 e m 1 x + c 2 x e m 1 x + c 3 x 2 e m 1 x + ....... + c k x k − 1 e m 1 x . In case if higher order differential equation has repeated conjugate complex roots. Then the general solution will be, y = c 1 e m 1 x + c 2 e − m 1 x + c 3 x e m 1 x + c 4 x e − m 1 x where m 1 represents an imaginary root. Calculation: Consider the differential equation 2 y ( 4 ) + 3 y ‴ + 2 y ″ + 6 y ′ − 4 y = 0 . Let y = e m x be a solution to the homogeneous differential equation 2 y ( 4 ) + 3 y ‴ + 2 y ″ + 6 y ′ − 4 y = 0

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

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Chapter 3, Problem 18CR

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To find: The general solution of the differential equation 2y(4)+3y‴+2y″+6y′−4y=0.

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Chapter 3, Problem 17CR

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Chapter 3 Solutions

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The general solution of the differential equation 2 y ( 4 ) + 3 y ‴ + 2 y ″ + 6 y ′ − 4 y = 0 .

Solution Summary: The author explains how to solve a higher-order differential equation.

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To find: The general solution of the differential equation 2y(4)+3y‴+2y″+6y′−4y=0.

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Chapter 3 Solutions