(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]y'=4e^{0.8x}-0.5y[/tex]

This question was obtained from a text book, where it is used as an example for the application of Heun's method (of ODE integration). They state that it has a 'simple' analytic solution of,

[tex]y=\dfrac{4}{1.3}(e^{0.8x}-e^{-0.5x})+2e^{-0.5x}[/tex]

2. Relevant equations

It is of the form.

https://www.physicsforums.com/latex_images/20/2024026-2.png [Broken]

3. The attempt at a solution

Attempted to use an integrating factor, https://www.physicsforums.com/latex_images/20/2024278-0.png [Broken]

https://www.physicsforums.com/latex_images/20/2024026-6.png [Broken]

Obtaining,

https://www.physicsforums.com/latex_images/20/2024278-1.png [Broken]

Hence,

https://www.physicsforums.com/latex_images/20/2024278-2.png [Broken]

Any ideas ?!?

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# Homework Help: Analytic solution of this ordinary differentiale equation

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