@Carl Love 

I don't intend to solve the equation, I just want to write commands that give me the coefficients. for exmaple coeffs command in polynomials...

@mmcdara 

tnx for your answer but i have problem with your two way, when I use first way I see warning:"Warning, (in anonymous procedure created in Typesetting:-FI) `m` is implicitly declared local"

and when I use second way I see Error: "Error, invalid sequence"

I work in Maple 2024.

@sand15 

Sorry, I didn't mean to get the derivatives of the function, I just want to write those expressions with for command in Maple. 

@acer thank you but unfortunately the shape is not displayed for me, I used Maple 2018.2 in windows, when I run your code in Maple I didn't any error and any figure. how can I solve this problem? with regards...

@Carl Love 

I ploted x^2+y^2 with plot3d and saw its figure but when run the your code for my question I didn't see figure that you earned.

@Carl Love 

thanks for your answer, I use Maple 2018 and changed the thickness value 0.1 to 0 but I didn't see any plot, where's the problem? tnx...

@Kitonum 

tnx my dear friend, this beautiful heart be for you. 

@Kitonum 

thank u, is there a way to express the result in serie(sigma) and if the condition was abs(1-x)>2 what would happen?

@Kitonum 

tnx for your answer. 

@RHERWOLF 

tnx for your answer, can you send me the Maple file here?

@Kitonum 

tnx, can I solve this below equation with this method:

eq := diff(F1(zeta), zeta, zeta)-b^2*F1(zeta)+2*exp(-b*zeta)*G1(zeta)+(exp(2*b*zeta)-2*exp(b*zeta)+1)*exp(-2*b*zeta)*(exp(b*zeta)*exp(-2*b*zeta)/(3*b)-(2*(exp(b*zeta)-1))*exp(-2*b*zeta)/(3*b))/(3*b^3)-(exp(b*zeta)-1)^2*(exp(-2*b*zeta))^2/(9*b^4)+(1/3)*(exp(b*zeta)-1)*exp(-2*b*zeta) = 0, diff(G1(zeta), zeta, zeta)-b^2*G1(zeta)-(exp(2*b*zeta)-2*exp(b*zeta)+1)*exp(-2*b*zeta)*exp(-b*zeta)/(3*b^2)-(2*(exp(b*zeta)-1))*exp(-2*b*zeta)*exp(-b*zeta)/(3*b^2)+b^2*exp(-b*zeta) = 0, 2*F1(zeta)+diff(H1(zeta), zeta) = 0
ics := F1(0) = 0, G1(0) = 0, H1(0) = 0, F1(infinity) = 0, G1(infinity) = 0

@nm 

tnx for the answer, I got this answer but I won't that inform limit, my answers must be:

@tomleslie 

alpha=sqrt((G*A)/(E*MI))

@acer 

thank you for your answer, I answer your questions hereunder:

I want to look for all the solutions and solve the system with the numeric method but when I use the fsolve command don't have all the answers and when using the solve command it takes a long time. is there any code, for example, Newton method code for solving it or I have to use the solve or fsolve commands? if I want to supposed to implement numeric rooting from scratch how can I do it?

with regards...

@Kitonum 

thank you, but is there any other command except solve & fsolve? because when numbers of my equations are increasing the solve command very takes a long time.

tnx...