Question

Hey @ganeshie8

Answer 1

I have to determine intervals which solutions are sure to exist, \[(x^2-4)y^{(6)}+x^2y'''+9y=0\] so since it's not an IVP could I still use the usual way, say our equation is \[y^{(6)}+\frac{ x^2 }{ (x^2-4) }y'''+\frac{ 9 }{ (x^2-4) }y=0\] and then I can set up \[a(x) = \frac{ x^2 }{ (x^2-4) }~~~~b(x) = \frac{ 9 }{ (x^2-4) }~~~~g(x) = 0\]

Answer 2

Then I can find an interval which it shares

Answer 3

So I guess, - inf <x <-2, -2<x<2, 2<x< inf

Answer 4

\[(- \infty , -2) \cup (-2,2) \cup (2, \infty)\]

Answer 5

it should not be an union, it should be exclusive
either this interval or that interval or that... right ?

Answer 6

The solutions are sure to exist either in \((- \infty , -2) \) or in \( (-2,2)\) or in \((2, \infty)\)

Answer 7

Ah, I had that at first, you're right!