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Sturm-Liouville misprint?

Hey,

I`m re-learning PDE`s, and there`s a section on ode`s with Sturm-Liouville equations, where one question says:

Verify the following is a S-L equation, and specify the type (regular, singular or periodic)

But, i think there might be a misprint in the equation. Here it is:

Unparseable latex formula:

2f ' ' (x)+f ' (x)+(\lambda+x)f(x)=0



but, breaking it up and then putting it into standard S-L form, the only form i can see which gives a S-L equation is:

(2xf′(x))′+xf(x)+λf(x)=0(2xf ' (x))'+x f(x)+\lambda f(x)=0

but the derivative of the 1st bracket doesn`t match the part with 1st and 2nd derivatives in the original equation!!

Can someone please confirm this must be a misprint, and they meant "2x" istead of just "x" , and the derivative of f to be multiplied by 2, - please!

(this is from page 55 of Solution Techniques for elementary PDE`s by Christian Constanda)
(edited 9 years ago)
Original post by Hasufel
...


Not something I've studied, so I could be wrong, but if you look at the opening page of texas.math.ttu.edu/~gilliam/ttu/ode_pde_pdf/Ch5.pdf in particular equations 5.1.1 and 5.1.2, if we apply an integrating factor of (e^(x/2))/2 I think it's doable as printed.

Depends what the book is expecting you to know/do, I suspect.
(edited 9 years ago)

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