Radius of convergence for (2+x²)y''-xy'+4y=0 about x₀=0

[SoulofLoneWlf]

quick help on this i seem to be missing some logic or process
determine the lower bound the radius of convergence of series solutions about the given X0

(2+x^2)y''-xy'+4y=0

xo=0

 

[nickmai123]

Well, we can't really help you unless you start the process. Do you have any idea where to go from here?

EDIT: If you've got absolutely no idea where to start, you should just Google "radius of convergence series solutions."

 

[SoulofLoneWlf]

Well, we can't really help you unless you start the process. Do you have any idea where to go from here?

EDIT: If you've got absolutely no idea where to start, you should just Google "radius of convergence series solutions."

well i was seeing that (2+x^2) has no discontinuity
so shouldn't the radius be infinity?

 

[nickmai123]

What does discontinuities of P(x) have to do with anything? A hint would be writing the DE in the form $$y^{''}+P(x)y^{'}+Q(x)y=0$$ and using a Fuchs' Theorem.

 

[SoulofLoneWlf]

What does discontinuities of P(x) have to do with anything? A hint would be writing the DE in the form $$y^{''}+P(x)y^{'}+Q(x)y=0$$ and using a Fuchs' Theorem.

thanks guys just hammered through it think i got my head around it :)