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Re: Help with an ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111286] Re: Help with an ODE
  • From: Sam Takoy <sam.takoy at yahoo.com>
  • Date: Mon, 26 Jul 2010 06:38:09 -0400 (EDT)
  • References: <i2btgu$bip$1@smc.vnet.net>

On 7/23/2010 7:13 AM, Sam Takoy wrote:
> I would GREATLY appreciate help symbolically solving the following ODE
> system.
>
> DSolve[y''[x] == (1 + y'[x]^2 + a y[x]^4)/y[x], y, x],
>
> with y[0] = y[1] = 1
>
> and "a" is a constant that satisfies
>
> Integrate[R[x]^2, {x, 0, 1}] = 1/(10*a);
>
> I can't quite pull it off with my current Mathematica skill level.
>
> Many many thanks in advance!
>
> PS: The solution is a smooth function that looks like a parabola.
>
> Thanks again!
>
> Sam
>

Hi,

May I just add that I would be very happy with a solution to

y''[x] == (1 + y'[x]^2 + y[x]^4)/y[x]

In other words, forget "a". I believe that the case a=1 has full generality.

Once again, I would greatly appreciate and help with solving this system.

Many many thanks in advance!

Sam


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