Question

@ganeshie8

Answer 1

Determine a lower bound for the radius of convergence of series solutions about each given point \(x_0\) for the given differential equation.
\[(x^2-2x-3)y''+xy'+4y=0\]

Answer 2

lower bound hmm?

Answer 3

lol *8

Answer 4

Haha, yeah and it seems 9 exists..

Answer 5

x'D

Answer 6

\[x_0 = 4, x_0 = -4, x_0 = 0\]

Answer 7

\[P(x) = x^2-2x-3~~~~Q(x) = x~~~~R(x) = 4\]

Answer 8

So what just check the distance from each x_0 ?

Answer 9

\[x-x_0\] where x is the singular point

Answer 10

I'd probably factor P(x)

Answer 11

Yeah (x-3)(x+1)

Answer 12

x=-1,3 and x = 0 for Q(x)

Answer 13

\[|x-x_0|?\] if that's all there's to it...

Answer 14

But for all cases? hmm

Answer 15

Beats me, I don't understand what the concept is here, just like what values you can pick so that P(x) is not zero? In that case, the lower bound will be the point to the left: