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Homework Statement
[itex]y''-2y+y=xe^xlnx[/itex]
The Attempt at a Solution
I don't know what I should do here because lnx. Is it possible to solve this ODE with undetermined coefficients method? how can I solve it?
Homework Statement
[itex]y''-2y+y=xe^xlnx[/itex]
The Attempt at a Solution
I don't know what I should do here because lnx. Is it possible to solve this ODE with undetermined coefficients method? how can I solve it?
Hi AdrianZ!
Sounds like a good plan.
Did you try the undetermined coefficients method?
As for the lnx, typically you can integrate that using integration by parts.
Try variation of parameters. http://en.wikipedia.org/wiki/Variation_of_parameters
It is quite easy in this case.
ehild
You applied exactly the method of "variation of parameters"I read the wikipedia page, I don't know what that method is, the wikipedia explanations are a bit confusing but I've already solved the ODE using the method where we take yp of the form v1y1+v2y2 and then we find v1 and v2 using a linear system of equations that are dependent to the derivatives of v's.
The thing is that the author has put this problem in the section of U.C method, so I'm wondering if he wants us to solve it using the undetermined coefficients method?
Hmm, as I see it both methods are basically the same.
No, they are basically different.
The method of undetermined coefficients uses trial functions. There are listed such ones for different types of functions on the right hand side in relation with the roots of the characteristic equation of the homogeneous part.See attachment.
ehild
Hey ehild!
I've just put your explanation and attachment to good use here:
https://www.physicsforums.com/showthread.php?t=554093
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And what is this method called? :tongue:
Let be y=ex Y.
Substituting into the ode, we get the equation Y"=xln(x), so Y=x3(6 ln(x)-5)/36, yp=exx3(6 ln(x)-5)/36.
ehild