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

- Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu,
- the textbook on Numerical Methods with Applications available from the lulu storefront,
- the textbook on Introduction to Programming Concepts Using MATLAB, and
- the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos

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