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**1. Homework Statement + relevant equations**

I have to solve

http://home.vs.moe.edu.sg/linl/eqn1.gif [Broken]

sigma, pinfinity, rho, N are constants. To make things easier for us, we are allowed to treat T as a constant.

**2. The attempt at a solution**

Treat T as constant:

http://home.vs.moe.edu.sg/linl/eqn2.gif [Broken]

At this point, this might help... Using a Maple-based solver, I get:

But I'm not sure how to read '_a = .. y)-t-C2 = 0' in symbolic.dsolve('Rho*(y*D2y+(3*Dy^2)/2)=-(pinf+(2*sig)/R-(N*T)/(R^3))')

Warning: Explicit solution could not be found; implicit solution returned.

> In dsolve at 312

ans =

Int(Rho*_a^2*R^2*3^(1/2)/(Rho*_a*R*(C1-2*_a^3*pinf*R^3-4*_a^3*sig*R^2+2*_a^3*N*T))^(1/2),_a = .. y)-t-C2 = 0

Int(-Rho*_a^2*R^2*3^(1/2)/(Rho*_a*R*(C1-2*_a^3*pinf*R^3-4*_a^3*sig*R^2+2*_a^3*N*T))^(1/2),_a = .. y)-t-C2 = 0

Anyway, moving along... using substitution:

http://home.vs.moe.edu.sg/linl/eqn3.gif [Broken]

I don't know how to proceed from here, but using the same solver,

Does anyone know how I can get to either solution or at least simplify the problem further from here? I don't know how to introduce an implicit solution into my working, too.y denotes U:

dsolve('Rho*(R*y*Dy+3*y^2/2)=-(pinf+2*sig/y-N*T/y^3)','R')

Warning: Explicit solution could not be found; implicit solution returned.

> In dsolve at 312

ans =

log(R)-Int(2/(2*N*T-3*Rho*_a^5-2*pinf*_a^3-4*sig*_a^2)*Rho*_a^4,_a = .. y)+C1 = 0

Thanks.

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