@Preben Alsholm 

Thanks very much for your assistance

@Preben Alsholm 

hi.1)at first i want the selected function as h1(theta) and h2(theta) ,....have a solution with zeros only at the end points not in the interior of the interval?(maximum in middle of interval not zero)

2)in ''h1(theta) = theta*(1-theta), h2(theta) = sin(Pi*theta), h3(theta) = theta*(1-theta), h4(theta) = theta^2*(1-theta)^2'' who i change scale??multiple in 10^13???

3)and in attached file for another eigenvalue please reform it.(we use

for b in extera .........)'' for another eigenvalue?

thanks

==============================================

for b in extra_bcs do try print(b = 1); res[b] := dsolve(`union`(`union`(`union`(newsys22, bcs), {bcs2}), {b = 1}), numeric, output = listprocedure, initmesh = 128, approxsoln = [omega2 = .956187059957729*10^13, h1(theta) = theta*(1-theta), h2(theta) = sin(Pi*theta), h3(theta) = theta*(1-theta), h4(theta) = theta^2*(1-theta)^2], abserr = 0.1e-2) catch: print(lasterror) end try end do; RES := res[((D@@3)(h2))(1)]; RES(0); plots:-odeplot(RES, [theta, h1(theta)], 0 .. 1)

@Preben Alsholm 

hi.thanks alot.1)due to different result for omega2 how i selected minimum of them??

2) why we consider only'' res[(D(h2))(1)](0),res[(D(h2))(0)](0),res[((D@@2)(h1))(0)],......''? and according what mention above how we thrust that omega2 which is gained is minimum ?(perhabs for example res[(D(h3))(1)](0) )

@Preben Alsho

thanks.....

1)by lines

''res[b] := dsolve(`union`(`union`(`union`(newsys2, bcs), {bcs2}), {b = 1}), numeric, output = listprocedure, initmesh = 128, approxsoln = [omega2 = 1, h1(theta) = theta*(1-theta), h2(theta) = sin(Pi*theta), h3(theta) = theta*(1-theta), h4(theta) = theta^2*(1-theta)^2], abserr = 0.2e-5)''

i couldnot gain omega2 as ''omega2 = 2.08*10^13''????

2)if i want solve this equation for another parameter dos not any way in maple??

thanks

@Preben Alsholm 

HI thanks.BUT i have two question;;

1)i want run this program for another set of parameter as A1,A2,A3,....for the reason i untill problem with determine omega2. to determine omega2 use 

''res[b] := dsolve(`union`(`union`(`union`(newsys2, bcs), {bcs2}), {b = 1}), numeric, output = listprocedure, initmesh = 128, approxsoln = [omega2 = 1, h1(theta) = theta*(1-theta), h2(theta) = sin(Pi*theta), h3(theta) = theta*(1-theta), h4(theta) = theta^2*(1-theta)^2], abserr = 0.2e-5)'' ????

2) how selected ''''''h1(theta) = 5*10^7*theta*(1-theta)*(1/2-theta), h2(theta) = 0.05, h3(theta) = 7*10^6*theta*(1-theta)*(1/2-theta), h4(theta) = 5*10^6*theta*(1-theta)*(1/2-theta)''''''????

@Preben Alsholm 

Hi Preben Alsholm.thank you very much for your good attention.I realized your idea for this purpose but i a little confused .I untill have a problem with the first guess of omega which you explain.may i demand you that apply your comments in attached file.because I for finding omega2=2.08*10^13 encounter with error.please kindness to me and apply whole of your comments in above attached file (error3.mw) .i am so sorry....  

error3_(3).mw

@farahnaz 

thanks.please explain that why in dsolve rule term union {b=1} dos not participation?

 and why amount of omega2 is selected as 2.0798272963267560997*10^13??

thanks

@Preben Alsholm 

thanks..but omega is unknown that require extra boundray condition

why method discution in ''

Different system  ,Commented: September 17 2015 

''

dosnot work??

i want to use it..

@Preben Alsholm 

hi.thanks a lot.i use former comments in another set equations but i encounter with error.please see equation and help me

thanks

error3.mw

@Preben Alsholm 

hi. thanks.but this assumption not allowed.however i apply your comments in my program and encounter with error.

please see..

thanks..is there another way for solve this equation??

1.mw

@Preben Alsholm 

hi.thanks.i see discussion in

http://mapleprimes.com/questions/204986-Dsolve-With-Unknown-Parameter#answer218470

and apply your comments in my program.note that in my program ''omega'' is unknown, which i use extera boundry condition.But in dsolve equations there is an error

please help me..thanks

error1.mw