Classical Solution Technique to Solve a First Order ODE

I have a audiovisual digital lecture on YouTube that shows the use of Euler’s method to solve a first order ordinary differential equation (ODE).  To show the accuracy of Euler’s method,  I compare the approximate answer to the exact answer.  A YouTube viewer asked me: How did I get the exact answer?

In this blog, I use the classical solution technique to find the exact answer to the ODE.  In a previous blog, I showed how to find the exact answer to the ODE by the integrating factor method.

Solving First Order Linear ODE by Classical Solution TechniqueSolving First Order Linear ODE by Classical Solution Technique

The pdf file of the solution is also available.

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Example: Solving First Order Linear ODE by Integrating Factor

I have a audiovisual digital lecture on YouTube that shows the use of Euler’s method to solve a first order ordinary differential equation (ODE).  To show the accuracy of Euler’s method,  I compare the approximate answer to the exact answer.  A YouTube viewer asked me: How did I get the exact answer?

In this blog, I use the integrating factor method to find the exact answer, because that is the method the viewer was using to solve the ODE exactly.  So here it is and in two future blogs, I will show the same example being solved by 1) Laplace transforms and 2) the classical (complementary + particular) solution techniques.
Solving First Order Linear ODE by Integrating Factor
Solving First Order Linear ODE by Integrating Factor

The pdf file of the solution is also available.

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2010 in review

The stats helper monkeys at WordPress.com mulled over how this blog did in 2010, and here’s a high level summary of its overall blog health:

Healthy blog!

The Blog-Health-o-Meter™ reads Wow.

Crunchy numbers

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A helper monkey made this abstract painting, inspired by your stats.

The Louvre Museum has 8.5 million visitors per year. This blog was viewed about 79,000 times in 2010. If it were an exhibit at The Louvre Museum, it would take 3 days for that many people to see it.

In 2010, there were 13 new posts, growing the total archive of this blog to 89 posts. There were 3 pictures uploaded, taking up a total of 1mb.

The busiest day of the year was October 28th with 441 views. The most popular post that day was MATLAB code for bubble sort.

Where did they come from?

The top referring sites in 2010 were numericalmethods.eng.usf.edu, autarkaw.com, newtonexcelbach.wordpress.com, google.com, and en.wordpress.com.

Some visitors came searching, mostly for bubble sort matlab, polynomial interpolation matlab, matlab solve equation, interpolation matlab, and spline matlab.

Attractions in 2010

These are the posts and pages that got the most views in 2010.

1

MATLAB code for bubble sort November 2009
1 comment

2

How do I solve a nonlinear equation in MATLAB? April 2009
7 comments

3

How do I differentiate in MATLAB? March 2009
1 comment

4

A Matlab program for comparing Runge-Kutta methods August 2008
4 comments and 1 Like on WordPress.com,

5

How do I do polynomial interpolation in MATLAB June 2009
1 comment