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.

The pdf file of the solution is also available.

This post is brought to you by

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

### Like this:

Like Loading...

## Published by

### Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.
View all posts by Autar Kaw

hi my name is Abdurrehman and in this course each topic must contain 4 to 5 example with solve one or two is not the soltion.So that people may understand each techniques

LikeLike

Data Transformation

I likewise believe thus, perfectly pent post Data Transformation

LikeLike

Awesome post . Thank you for, posting on this blog mate! I shall message you soon! I did not realise that.

LikeLike

I like your tutorials. Please help me get a textbook of ordinary/ differential equation

LikeLike

which is the best book concerning this problems

LikeLike

Any introductory ode book would do.

LikeLike

I want to solve any mathematics calculation using c3 mobile phone

LikeLike

give us more complicated example because that one was very easy.

LikeLike

give us more compilcated example it was so easy

LikeLike