MHB Find Ansatz for this ODE (3.5.15)

[ognik]

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

 

[MarkFL]

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?

 

[ognik]

Copied OK, probably typo in book - if the driving function was just $e^x$ it would be more sensible