Thanks for your insight sir.

I need real solutions. Here's my whole set of equations. I tried using Newton's method to solve nonlinear equations a2 and a3 and now trying to work on nonlinear differential equation a1.
I am struggling with these three equations.
The first is a nonlinear equation which can be solved numerically with the boundary conditions y(infinity)=0 and y'(0)=0.
a1 := diff(y(r), r, r) = -2*(diff(y(r), r))/r-1.3*10^12*polylog(3/2, exp(b(u-y(r))))
Now y(r) depends parametrically on u and b which can be determined using these equations:
a2 := -1.5*10^8*(int((3*polylog(5/2, exp(b(u-y(r))))/b^(5/2)+y(r)*polylog(3/2, exp(b(u-y(r))))/b^(3/2))*r^2, r = 0 .. 10)) = -129000
a3 := 3*10^8*(int(r^2*polylog(3/2, exp(b(u-y(r)))), r = 0 .. 10))/b^(3/2) = 1
Again really appreciate your help.
Thanks
MS

Hi Robert,
thanks for all the input and help so far.
I have this nonlinear differential equation with boundary conditions. I have tried quite few ways but nothing seems to be working .
x := diff(y(r), r, r)+2*(diff(y(r), r))/r+1.5*(16*4300)*Pi^2*10^6*sqrt(Pi/(2*0.128e-2^3))*polylog(3/2, exp(0.128e-2*(1194.3-y(r)))) = 0;
boundary conditions: bc:= D(y)(0) = 0, y(infinity) = 0
Thanks in advance
MS

I checked my equations and I was missing a component in the denominator. Sorry for that. Now these are my equations (thoroughly checked ) and on Robert's advice converted to x.
y1 := (1000*(16*Pi^2*1.5)*10^6*sqrt(pi/(2*b^3))*(1/3))*(((2/3)*x+3/4)*(ln*x)^(3/2)/(1+x)+(3/2)*(ln*x)^(1/2)*ln(1-ln*x)) = 1
y2 := -(1000*(8*Pi^2*1.5)*10^6*sqrt((1/2)*pi)*(1/3))*(3*((2/5)*(ln*x)^(5/2)/(1+exp(-ln*x))+(ln*x)^(5/2)/(1+x)+(5/2)*(ln*x)^(3/2)*ln*(1+exp(-ln*x))-(3/4)*(ln*x)^(3/2)/(1+x))/b^(5/2)-4300*(((2/3)*x+3/4)*(ln*x)^(3/2)/(1+x)+(3/2)*(ln*x)^(1/2)*ln(1-ln*x))/b^(3/2)) = -129000
If i try to solve them, i get 'solutions may have been lost'.
Thank you all for your help
Manjeet
If i try to solve them, i get 'solutions may have been lost'.

These are my actual two nonlinear equations. If the above equations do not have closed form solutions, that is probably due to some approximations I made.
eqn1 := 1.4*10^8*(int((3*polylog(5/2, exp(b*(u-4300)))/b^(5/2)+4300*polylog(3/2, exp(b*(u-4300)))/b^(3/2))*r^2, r = 0 .. 10)) = -1290
eqn2 := 2.4*10^8*(int(r^2*polylog(3/2, exp(b(u-4300))), r = 0 .. 10)) = 1
I am trying to solve these two equations for b and u from last one week..
Any advice is welcome...
Thanks again for your time
Manjeet

Thanks man for your advice....but fsolve is not spitting out solutions...it's just giving the same equations as output.....