General Solution for y''+(1/x)y'=0: Proving Boundedness

[sara_87]

Homework Statement

Find the general solution of: y''+(1/x)y'=0
and show that only constant solutions are bounded.

Homework Equations

The Attempt at a Solution

integrating factor say a=e^(int(1/x)dr)=x
so xy''+y'=0. so (xy')'=0
integrate both sides: xy'=c (c is a constant)
integrate again: y=cln(x)+d (d is a constant)

but i don't know how to show that only constant solutions are bounded.
Thank you

 

[tiny-tim]

Hi sara_87!

Find the general solution of: y''+(1/x)y'=0
and show that only constant solutions are bounded.
…
y=cln(x)+d (d is a constant)

but i don't know how to show that only constant solutions are bounded

But you're there …

ln(x) is unbounded, isn't it?

 

[sara_87]

Oh right so this means only the solutions y=d can be bounded, right?
Also, there's a similar question:
find the general solution of: y''=0 and show that only constant solutions are continuous.

general solution i found to be: y=cx+d (again c and d are constants)
but in this case, why can only constant solutions be continuous?

 

[tiny-tim]

find the general solution of: y''=0 and show that only constant solutions are continuous.

general solution i found to be: y=cx+d (again c and d are constants)
but in this case, why can only constant solutions be continuous?

dunno

must be a misprint ​

 

[sara_87]

:)
It's not a misprint.
Never mind.
Thank you.