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