Repeated roots in ordinary differential equation – next independent solution – where does that come from?

When solving a fixed-constant linear ordinary differential equation where the characteristic equation has repeated roots, why do we get the next independent solution in the form of x^n*e^(m*x)?  Show this through an example.

See this pdf file for the answer.

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Machine Epsilon – Question 4 of 5

In the previous blog posts, we answered

Here we answer the next question.

Future post will answer this last question
Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?
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Machine epsilon – Question 3 of 5

In the previous blog posts, we answered

Here we answer the next question.
Machine epsilon
Future posts will answer these questions
Question 4 of 5: What is the significance of machine epsilon for a student in an introductory course in numerical methods?
Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?
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Machine epsilon – Question 2 of 5

In the previous blog post, we answered

Here we answer the next question.

Machine epsilon

Future posts will answer these questions
Question 3 of 5: How is machine epsilon related to the number of bits used to represent a floating point number?
Question 4 of 5: What is the significance of machine epsilon for a student in an introductory course in numerical methods?
Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?
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Machine epsilon – Question 1 of 5

Future posts will answer these questions

Question  2 of 5: How do I find the machine epsilon using a MATLAB code?Question 3 of 5: How is machine epsilon related to the number of bits used to represent a floating point number?Question 4 of 5: What is the significance of machine epsilon for a student in an introductory course in numerical methods?Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?________________________

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A Facebook Page for Numerical Methods

We have started a Facebook page for numerical methods. I welcome you to join the group and spread the word about it.  Ask a question and stay updated with new resources.

https://www.facebook.com/numericalmethods

The Facebook page would be a place to keep the social media conversation going on – the one that has been going on via YouTube comments, twitter and this blog.

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Reconciling secant method formulas

Depending on how you derive the secant method, one gets the final formulas that are the same but the form is different.  This blog shows one how to reconcile the formulas.

Reconciling secant method formulas
Reconciling secant method formulas
Reconciling secant method formulas

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