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Re: Solving Third Order differential equation using Mathematica.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg127378] Re: Solving Third Order differential equation using Mathematica.
*From*: "Nasser M. Abbasi" <nma at 12000.org>
*Date*: Fri, 20 Jul 2012 23:38:59 -0400 (EDT)
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*Reply-to*: nma at 12000.org
On 7/20/2012 2:53 AM, amitesh wrote:
> Hi,
>
> I am trying to solve a third order differential eqn in mathematica.
> DSolve[{1/30 f'''[x] - f[x] (2 a^3/(1 - x a)^3 + 1/(1 - x)^3) - 24 a/
> (1 - y) (1/(1 - x)^7 - a^5/(1 - ax)^7) == 0, f[0] == 0,
> f''[0] == 0}, f[x], x]
> I am running this eqn for last 1 hour :/ why does Mathematica take so
> much time?
>
I do not know why. It looks like a hard ODE.
But let start first by fixing few error in your code
1) ax should be a*x
2) a third order initial conditions ODE will have 3 initial conditions
(unless you wanted to obtain constants for these. But since you provided
IC for f[0] and f''[0], then this tells me you missed an IC for f'[0] ?
3) what exactly is 'y' above? this is used as a parameter like 'a'. Then
using 'y' for a parameter is a really bad choice for a symbol. Use 'b'
or 'c'. That is the standard.
4) it is a hard ode. For some conditions on 'a' and 'y', you'll can get singularity.
Try adding assumptions on the parameters to see if this helps. But
why not simply try NDSolve. Why do you have to have an analytic solution?
NDSolve tells me this is a stiff ODE as well.
--Nasser
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