find an interval centered about x = 0

**slapmaxwell1** · February 25th 2011, 06:56 PM

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?

**chisigma** · February 25th 2011, 08:52 PM

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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