Question: Nonlinear 2nd order ode

Hi,

I used the dsolve command mentioned by Maple experts in the earlier blog to solve the following ode with bcs.

ode:= diff(y(x),x$2) + 1/x *diff(y(x),x) + 0.6*y(x) + y(x)^3 - y(x)^5  = 0

bcs:= D(y)(0) = 0,   y(d/2) = 0.8 * y(0)

The ode is a spherical coordinate system. The radius is defined by ‘x’ and the diameter by 'd'. 

The ode is solved for different diameter values ‘d’ of sphere and plotted as variation of y(x) with x/(d/2) i.e. radius/diameter of sphere. The attached figure is an jpg of the results from the journal paper.

When I try to solve the above ode, i do not get the match with the results from the paper. I also find difficulty in plugging the second boundary condition.

Could you please help me in solving the above ode to get following figure? I spent two whole days, but in vain. One more thing to mention is that the authors of the papers used finite difference method? would the method of solving ode matter?

Thanks in advance,

rpd