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I need to solve a differential equation for my bachelor's project. Rather i need to find a asymptotic solution, when x goes to infinity.

That eq. describes Alfven Waves in rotating inhomogenious plasmas, accounting effects of finite larmor radius.

So the equation is as follows:

[tex]f'''(x)+xf'(x)+\frac{3}{2}f(x)=0[/tex]

I made some research and I found that such equations are actually studied, but unfortunaly I can find the articles, which concern such an equation.

First article is:

Pfeiffer, G. W. Asymptotic solutions of y"'+qy'+ry=0. J. Differential Equations 11 (1972), 145-155.

Where q and r are some functions of x.

Second:

Hershenov, J. Solutions of the Differential equation y"'+ay'+by=0. Stud.

Appl. Math. 55 (1976), 301-314.

Where a and b are some constants.

The second article more likely matches my needs.

Also i know that equaion

[tex]f'''-4xf'-2f=0[/tex]

which differs from mine only with constants, is Generalized Airy's Equation, and whose solution is well known and is expressed through products of Airy's functions.

If anyone can help me with this eq., or if you could find one of those article it would help my diploma very much!

thx for your concideration.

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# 3rd Order differential eq.

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