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Math Help - find an interval centered about x = 0

  1. #1
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    find an interval centered about x = 0

    find an interval centered about x=0 for which the given initial value problem has a unique solution.

    (x-2)y'' + 3y = x, y(0) , y'(0)=1

    ok so my book is saying that because a2(x)=x-2 and x0 =0 the problem has a unique solution for -infinity<x<2.

    im not understanding why this is the answer?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Writing a second order linear DE as...

    \displaystyle a_{2}(x)\ y^{''} + a_{1}(x)\ y^{'} + a_{0} (x)\ y = b(x) (1)

    ... it has only one solution for x in [a,b] if in that interval is a_{2}(x) \ne 0 ...

    Kind regards

    \chi \sigma
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