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Bounded solutions

  • Thread starter sara_87
  • Start date
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1. Homework Statement

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

2. Homework Equations



3. 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 dont know how to show that only constant solutions are bounded.
Thank you
 

tiny-tim

Science Advisor
Homework Helper
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Hi sara_87! :smile:
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 dont know how to show that only constant solutions are bounded
But you're there

ln(x) is unbounded, isn't it? :wink:
 
763
0
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

Science Advisor
Homework Helper
25,790
246
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 :confused:

must be a misprint :redface:
 
763
0
:)
It's not a misprint.
Never mind.
Thank you.
 

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