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| ``Re: Solving second order linear ODE''
by perucho on 2009-11-06 02:54:42 |
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| Well curious, you need to know some math topics in order you may solve your ODE.
1.- What's the interval a<x<b where your ODE is defined? In this sense when I gave you the function R(x), take the limits of integration
R(x) = e^{\int_a^x P(x)dx} ('a' being the lower and 'x' upper one)
Also P(x) and Q(x) must be continuous in (a,b).
2.- You also need a boundary conditions, for instance, u(a) and u'(a). If u(a)=u'(a)=0, you fall in a Sturm-Liouville problem, and therefore you also need to know about Bessel and Fourier technics.
3.- The most expedite way you can solve your ODE, I think, is via Green functions.
As stated, your problem is quite general.
I don't know what's your level in those questions, so let me recommend to you one out of my old books:
H.F. Weinberger, Partial Differential Equations, Blaisdell Publishing Co., NY(Congratulations by their 27!).
Or better, you go to your College's Library and find out by newer books about those topics.
Good Luck!
perucho |
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