manjees

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10 years, 101 days

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These are answers submitted by manjees

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.....
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