Solution Found!
By using Newton’s method or some other numerical procedure
Chapter 4, Problem 45E(choose chapter or problem)
By using Newton's method or some other numerical procedure to approximate the roots of the auxiliary equation, find general solutions to the following equations:
(a) \(3 y^{\prime \prime \prime}+18^{\prime \prime \prime}+13 y^{\prime}-19 y=0\) .
(b) \(y^\text{iv}-y^{\prime \prime}+5 y=0\) .
(c) \(y^\text{v}-3 y^\text{iv}-5 y^{\prime \prime \prime}+15 y^{\prime \prime}+4 y^{\prime}-12 y=0\) .
Equation Transcription:
Text Transcription:
3y’’’+18’’’+13y’-19y=0
y^{iv}-y’’+5y=0
y^{v}-3yiv-5y’’’+15y’’+4y’-12y=0
Questions & Answers
QUESTION:
By using Newton's method or some other numerical procedure to approximate the roots of the auxiliary equation, find general solutions to the following equations:
(a) \(3 y^{\prime \prime \prime}+18^{\prime \prime \prime}+13 y^{\prime}-19 y=0\) .
(b) \(y^\text{iv}-y^{\prime \prime}+5 y=0\) .
(c) \(y^\text{v}-3 y^\text{iv}-5 y^{\prime \prime \prime}+15 y^{\prime \prime}+4 y^{\prime}-12 y=0\) .
Equation Transcription:
Text Transcription:
3y’’’+18’’’+13y’-19y=0
y^{iv}-y’’+5y=0
y^{v}-3yiv-5y’’’+15y’’+4y’-12y=0
ANSWER:
Solution
Step1:
In this problem, we have to solve the general solution of the given equation with newton’s law method .