## 360 Reputation

13 years, 51 days

## I need real solutions....

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

## nonlinear differential equation...

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...

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...

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...

Thanks man for your advice....but fsolve is not spitting out solutions...it's just giving the same equations as output..... 1 2 3 Page 3 of 3
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