# Math Help - find an interval centered about x = 0

1. ## 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?

2. 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

$\chi$ $\sigma$