Using Mathematica to Solve a Complicated Initial Value Problem

Hi All,

So I've encountered a monster of an initial value problem that I've been trying to solve with Dsolve in Mathematica, with not much success (Headbang).

Here is what the IVP looks like:

$\frac{d}{du}((-G^3 \frac{dG}{du})^\frac{1}{m+2}) - \frac{d}{du}(uG) + (\frac{m+2}{m-2})(\frac{1}{\alpha}- \frac{5}{m+2})G$

With the following extra information(initial conditions) :

$G(0) = 1$

and

$(-\frac{dG(0)}{du})^\frac{1}{m+2} = (\frac{m+2}{m-2})(\frac{1}{\alpha} - \frac{5}{m+2})$ $\int_{0}^{\lambda} G(u)~du$

I've also attached my attempt to this post - AshProblem.pdf. Unfortunately, I wasn't able to upload a .nb file.

Any help/guidance would be greatly appreciated.

Thanks