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    Given that u(r) = a(r^-2) + b(r^3) (where r is a radial coordinate), I need to find values of a and b such that u(r) is "finite throughout the region r<1" and du/dr is -6 at r=1.

    I've done the second part and found that 2a-3b=6, but I don't understand what it means by finite when r<1. It seems that r will only not be finite when r=0, but this will be the case whatever the values of a and b...

    Any help would be appreciated.
    Thanks.
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    (Original post by ryanwilk)
    Given that u(r) = a(r^-2) + b(r^3) (where r is a radial coordinate), I need to find values of a and b such that u(r) is "finite throughout the region r<1" and du/dr is -6 at r=1.

    I've done the second part and found that 2a-3b=6, but I don't understand what it means by finite when r<1. It seems that r will only not be finite when r=0, but this will be the case whatever the values of a and b...

    Any help would be appreciated.
    Thanks.
    Look for values of r for which your soln is undefined/infinite and think how to remove them.

    just read your post properly. which part of your soln causes it to be undefined at r=0? then do something to get rid of it.
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    (Original post by thebadgeroverlord)
    Look for values of r for which your soln is undefined/infinite and think how to remove them.

    just read your post properly. which part of your soln causes it to be undefined at r=0? then do something to get rid of it.
    I was thinking that maybe if a is zero, it would be finite, but then you have 0/0 which seems a bit wrong...
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    (Original post by ryanwilk)
    I was thinking that maybe if a is zero, it would be finite, but then you have 0/0 which seems a bit wrong...
    if a = 0 where does 0/0 come from?
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    If r is zero as well then a(r^-2) will be 0/0. Or does r being a radial co-ordinate mean that r can't equal zero?
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    (Original post by ryanwilk)
    If r is zero as well then a(r^-2) will be 0/0. Or does r being a radial co-ordinate mean that r can't equal zero?
    If you chose a=0 then u=br^3 which is a soln of the ODE. 0/0 never comes into it.
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    Ah ok, I see what you mean.
    Thanks for the help.
 
 
 
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