MHB Find Ansatz for this ODE (3.5.15)

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The discussion revolves around finding an appropriate Ansatz for the ordinary differential equation (ODE) $y'' + y' - 2y = \frac{e^{x}}{x}$. Participants note that the particular solution may not be expressible in elementary functions, raising concerns about the accuracy of the problem statement. A potential typo in the book is suggested, as a simpler driving function like $e^x$ would be more manageable. The conversation emphasizes the importance of verifying the problem's details before proceeding with solution attempts. The complexity of the given ODE indicates that specialized methods may be required for an accurate solution.
ognik
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Hi - I'm given: $ y'' + y' - 2y = \frac{e^{x}}{x} $

What is a good Ansatz to find the particular solution? I've tried a few that haven't worked...Thanks
 
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ognik said:
Hi - I'm given: $ y'' + y' - 2y = \frac{e^{x}}{x} $

What is a good Ansatz to find the particular solution? I've tried a few that haven't worked...Thanks

According to W|A, the particular solution is not expressible in terms of elementary functions. Are you certain you have the problem copied correctly?
 
Copied OK, probably typo in book - if the driving function was just $e^x$ it would be more sensible
 

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