Explanation Given: The given equation is 2 y ″ ′ − 3 y ″ − 12 y ′ + 20 y = 0 . Approach: Determine the roots of the auxiliary equations to find the general solution of the equation. Calculation: Consider the given differential equation. 2 y ‴ − 3 y ″ − 12 y ′ + 20 y = 0 The auxiliary equation of above differential equation is, 2 r 3 − 3 r 2 − 12 r + 20 = 0 Solve the above equation. 2 r 3 − 3 r 2 − 12 r + 20 = 0 ( r − 2 ) 2 ( 2 r + 5 ) = 0 r = 2 , 2 , − 5 2 The roots r 1 , r 2 and

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 4.RP, Problem 12RP

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The general solution of the given equation 2y″′−3y″−12y′+20y=0.

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The general solution of the given equation 2 y ″ ′ − 3 y ″ − 12 y ′ + 20 y = 0 .

Solution Summary: The author analyzes the auxiliary equations to find the general solution of the given equation.

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The general solution of the given equation 2y″′−3y″−12y′+20y=0.

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Chapter 4 Solutions

The general solution of the given equation 2 y ″ ′ − 3 y ″ − 12 y ′ + 20 y = 0 .

Solution Summary: The author analyzes the auxiliary equations to find the general solution of the given equation.

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To find: The general solution of the given equation 2y″′−3y″−12y′+20y=0.

Want to see the full answer?

Chapter 4 Solutions

To find:

The general solution of the given equation 2y″′−3y″−12y′+20y=0.