Behavior at zero and at infinity

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    Behavior Infinity Zero
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SUMMARY

The discussion focuses on analyzing the behavior of a second-order differential equation (DE) with singularities at zero and infinity. To approximate the behavior near x = 0, the approach involves retaining only the dominant terms as x approaches zero and simplifying the equation. For the singularity at infinity, a variable change to u = 1/x is recommended, allowing for analysis around u = 0. These methods provide a clear pathway to understanding the behavior of the DE at critical points.

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intervoxel
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Hi,

I have a second order DE involving the first derivative and with singularities at zero and at infinity. I need the approximate behavior at zero and at infinity. I have the answer but I would like to know how to get there.

I don't know how to start this search. Any help?
 
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For the singularity near x = 0 I would try keeping only the largest terms as x -> 0 and solve the simplified equation.

For the singularity near x = infinity, I would try to change variables to u = 1/x, and then do the same thing around u = 0.
 
Bingo! Thanks a lot.
 

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