How can I get an asymptotic solution for 2nd order differential equation.
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For the 2nd order differenttiaal equation:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/201940/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/201941/image.png)
How can I get an asymptotic solution, where
for z=0. Thanks for the help.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/201951/image.png)
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David Goodmanson
2019-2-1
编辑:David Goodmanson
2019-2-1
HI Dereje,
There seems to be inconsistency about M^2 vs. M, so it's preferable to quit M and use Torsten's notation for a starting point:
u'' = c u^(1/4)
LIke a lot of differential equations you assume a solution and verify that it works. (It was kind of exasperating sometimes in the diffyq course, when the instructor would put up some differential equation, pull a hypothetical solution out of the air and say, let's see if this works. Which of course it always did). Anyway, assume u = a z^n, plug that in, get
n(n-1) z^(n-2) = c (a z^n)^(1/4) = c a^(1/4) z^(n/4)
Equate powers of z on each side, find out n = 8/3. Equate coefficients in front on each side and you can solve for a. You get one solution for positive z that way, and you can see that in trying to find others, expansion in powers of z^(8/3) makes some sense
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