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Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution.

I've been trying to do this tute question,

http://img848.imageshack.us/img848/8382/sdfsq.jpg [Broken]

but in my lecture note we only went through the proofs of how the solutions are linearly independent and so on,

Would anyone be able to point we in the right direction to where I can find some examples of ODE's like this, solved without already knowing a particular solution?

I have spent some time trying to guess one of the solutions so I could find the other but it isn't going so well,

Mathematica spits out ((1 + x^2) C[1])/(2 x) + (i(-1 + x^2) C[2])/(2 x)

as the general solution but without knowing how it got there it doesn't really help,

Thanks

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# Homework Help: 2nd Order Linear homog ODE of variable coefficients

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