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Re: non-linear differential equations.

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  • Subject: [mg16144] Re: [mg16108] non-linear differential equations.
  • From: "Richard Finley" <rfinley at>
  • Date: Sat, 27 Feb 1999 03:23:10 -0500
  • Sender: owner-wri-mathgroup at


Do you mean:

p - 2^(n-1)(1-beta[z])(1+beta[z]+beta[z]^2)^(n-1) == 1/(Ca r[z])

as your equation implies when rewritten or was it supposed to be

p - 2^(n)(1-beta[z])(1+beta[z]+beta[z]^2)^((n-1)/2) == 1/(Ca r[z])   

regards, RF

>>> <engp7696 at> 02/25/99 07:25AM >>>
While using Mathematica I have a problem with the solution of the
following non-linear differential equation:

p - 2^n (1 + beta[z])(1 + beta[z] + beta[z]^2 )^(n-1)/2 == 1/(Ca r[z] )


n = is a constant ranging from -infinity to + infinity;
p = constant = 2^n (n+2)
beta[z] = z r'[z]/r[z]
Ca = constant

The boundary condition is
r[z = 3200] = 10^(-10)

I need to obtain a plot of r vs z.

The problem is
	1)NDSolve seems to be working only when (n-1)/2 is a whole
	number . i.e for n = 3, 5, 7 etc.
	2)NDSolve does not work for n < 3 or when (n-1)/2 is not a whole
	3)Even when NDSolve works for n = 3, 5, 7 etc I also obtain
	imaginary solutions.

	This equation has been solved by finite difference methods with no
problems using a BASIC code.

I would like to know if there is any fool-proof method to solve the
problem in Mathematica for all n without obtaining imaginary solutions.

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