@Markiyan Hirnyk 

thanks..how i can gain another polynomials that have at least one amount zero in interval [0..1]

afther this have two amount zero at two point in interval[0..1]

and so on ,respectively?

former polynomial dos not have amount zero in the interval [0..1] and ploted as below:

for example i want this polynomials have such graph as below....thanks

case2:

case3:

@Markiyan Hirnyk 

thanks

@Markiyan Hirnyk 

I would be grateful if you could solve my problem .     

@Markiyan Hirnyk 

insert the body of the question again..EQ.mw

@Markiyan Hirnyk 

hi.above link dos not work

please chek it

thanks

@acer 

thanks

@Axel Vogt 

@Axel Vogt 

thanks..is only due to numeric integral which is used?

by this method running need to much time !!!

is there any way?

thanks

@Preben Alsholm 

Mr Preben Alsholm  may i asked you for answer to me?please

thanks alot

@Preben Alsholm 

by different value of abserr i can not reach in to the answer.please tell me about its value?

do i change more in the code program  for gettting answer?

thanks

@tomleslie 

thanks.i dont really should {b=0} or not but we need non trial solutions and i think that b should not equal to zero...because  my equations have unknown parameter ''omega'',we use extra boundary conditions untill by using dsolve in maple we can reach to the answer.in general my equations are in the group of eignvalue  problems..

@tomleslie 

thanks..how i can command  third set of boundary conditions in dsolve ? 

@Preben Alsholm 

YES. right with you and i apologize of you .i apply your comments , but encounter again  error BOUNDARY_CONDITION2.mw

please check it 

thanks alot

@Preben Alsholm 

hi.mr Preben Alsholm  i and torabi both work on this equations.as my co worker told you value of L is:

L := 1/500000000.

also we reach to the result according attached file below, but seems boundary condition not satisfy!!

please tell us the reason?? because the graph of g1,g2 and g3 is not symmetric about x axis.

BOUNDARY_CONDITION.mw

thanks

@tomleslie 

by  defining N:=infinity i encounter with problem in next calculation..