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Help with an ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111205] Help with an ODE
  • From: Sam Takoy <sam.takoy at yahoo.com>
  • Date: Fri, 23 Jul 2010 07:13:53 -0400 (EDT)

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


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