@Preben Alsholm 

why Y is not apply on matrix and shown in final result?

maple2modif.mw

@Preben Alsholm 

thanks.i apply your good comments but now i have a problem for integral.please help me

thanksmaple2.mw

@Carl Love may i solve it in mathematica or matlab?

@Preben Alsholm 

thanks ..whole boundary conditions attached as figure below.

perhaps i have error for writing them!!

please see them

thanks..

@Carl Love 

thanks..i correct program which reload again.really  f3(x)*h=w(x, theta)2D.mw

this equation due to this terms are nonlinear

""""""400/((1-W(x, theta))*ln(10-10*W(x, theta))^2)-500/(1-W(x, theta))^4"""""

thanks

@Preben Alsholm 

L := 1/500000000

value of L was defined in code (restart; Digits := 30; L := 1/500000000       .....  )

@Preben Alsholm 

hi.due to  comparison the result i decided that remove nonlinear terms.because the result which is obtanied , not mached with correct result.major problem for me is  initial guess and dependent eginvalue to approxsol in maple!!!!!this makes that i donot know which answer is correct!!

@Preben Alsholm 

hi.thanks.is there analytic solution by removing non linear term.if possible please help

thanks a lot

@Preben Alsholm 

hi.thanks.i apply your good comments in maple code, but result, which i gain for omega1 and omega2 are omega1=34.03 and omega2=824, but i can not to reach them...i tried to gain them,but i failed.how i reach to the correct omega?in numeric method i guess that initial amount for approxsol is very important.may we able to solve eignvalue throgh another way i.e. by nontrial solution which obtaned by zero determinant?in other word may we solve analytical and gain omega?in this method because there are many eignvalue , how we selected corret non linear ferquency of physical system such as beam in this maple code?

thanks alot

two_unkown.mw

@torabi 

hi .thanks.please explain to me,how i can  calculate eignvalues analytically not numerically in maple file which attached  before..... 

thanks alot.is there any way for this?

@Preben Alsholm 

hi.thanks

by changing amount of omega2 in line ''''''approxsoln = [omega2 = 1000, f(x) = x^2*(1-x)^2]....''''

different result is obtained.how i can chose one of them?

on the oder hand how determine initial guess for omega2(for examole 1000 in above line) which whole of the eigenvalues  are identical  for different extra boundry conditions?

thanks

@Preben Alsholm 

thanks alot

@Preben Alsholm 

hi....according attached file 

res dos not any answer and the following rule''    indx := indices(res, nolist)''

encounter with '' 

Error, invalid input: indices received res, which is not valid for its 1st argument, t''.

How i can remove it and gain solution for res ??

In the other word for gain unknown parameter (lambda), dsolve for extra boundray condition hsa no any answer for 

{(D(f1))(0), (D(f1))(1), (D(f4))(0), (D(f4))(1), (D(f6))(0), (D(f6))(1), ((D@@2)(f1))(0), ((D@@2)(f1))(1), ((D@@2)(f2))(0), ((D@@2)(f2))(1), ((D@@2)(f3))(0), ((D@@2)(f3))(1), ((D@@2)(f5))(0), ((D@@2)(f5))(1), ((D@@3)(f2))(0), ((D@@3)(f2))(1), ((D@@3)(f3))(0), ((D@@3)(f3))(1), ((D@@3)(f5))(0), ((D@@3)(f5))(1)}???

thanks..

22.mw

@Preben Alsholm 

attached file

22.mw

@Preben Alsholm 

hi.i am really sorry.i apply your comments in my code and study what you said before to the  user such as farahnaz ,....

but at the end of code , i encounter with '''''

initial approximation matrix must contain variable names'''''

and error 

'''''Error, invalid input: indices received res, which is not valid for its 1st argument, t''''''