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# Differential Equation question watch

1. 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.
2. (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.
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...
4. (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?
5. 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?
6. (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.
7. Ah ok, I see what you mean.
Thanks for the help.

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