# 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.

The pdf file of the solution is also available.

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## Author: 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.

## 10 thoughts on “Example: Solving First Order Linear ODE by Integrating Factor”

1. Abdurrehman says:

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

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

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3. KUDZE MENSAH KWAKU says:

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

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4. Hussein Owayo says:

which is the best book concerning this problems

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5. Hussein says:

I want to solve any mathematics calculation using c3 mobile phone

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6. abdul qayyum says:

give us more compilcated example it was so easy

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