Problem with linken general differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg52703] Problem with linken general differential equations
• From: Roger Bagula <tftn at earthlink.net>
• Date: Thu, 9 Dec 2004 20:23:35 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```This is a generalized Hermite-Bessel problem ( on the substitution of
x->1/x):
NSolve[{f''[x]+(a+b*x^n)*f[x]==0,f''[1/x]+(a+b*x^(-n))*f[1/x]==0},f[x],x]
The solutions for n=2 as separate equations like:
NSolve[f''[x]+(a+b*x^2)*f[x]==0,f[x],x]
NSolve[f''[x]+(a+b/x^2)*f[x]==0,f[x],x]
work , but n=3 I can't get to solve.
NSolve[f''[x]+(a+b*x^3)*f[x]==0,f[x],x]
NSolve[f''[x]+(a+b/x^3)*f[x]==0,f[x],x]
and with that I don't think
the general solution has been found either.
Any help would be apprciated.

Respectfully, Roger L. Bagula

alternative email: rlbtftn at netscape.net

```

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