@Preben Alsholm 

thanks.yes my problem was about ''Division by zero.''

i reform that line as 

bcs2 := eval[recurse](convert(ds[1], D), `union`({y = 1}, bcs3))..

and also multipy whole of three equations by term ( x^4), but encounter error

"initial Newton iteration is not converging".i try to remove this error, but i failed.

please see it.also in this equations i have some terms with scale 10^(-27).if i define digite :=15,then  the result which are gained finally are coorect?not_converging.mw

thanks...

@Preben Alsholm 

thanks...

@Preben Alsholm 

thanks.because of taking extra boundary condition for determine parameter omega, is this method similar to shooting method?

thanks

@iman 

hi.my question is about method for finding unknown parameter omega?

name of this method is my quedtion.

thanks

@Preben Alsholm 

thanks... i reach in answer with out any error.
but My aim is about each methods ,in which unknown parameter (omega) is drived, not in dsolve?

@iman 

hi.according latest common by mr Preben Alsholm, i encounter with error: 

"input system must be an ODE system, got independent variables %1", {`1`, y} '

for dsolve 4 equations.please guide me.thanks alot

d1.mw

@Preben Alsholm 

thanks very very  alot mr Preben Alsholm..

may i know the name of this numerical method ? is this shooting method?

and at the end  for example  if my numbers be in domain   (10^(-50) to 10^(50)) or higher ,should i change some lines in recent code?  for example change Scaling omega2 , maxmesh,Digits and abserr,  ....??

thanks

@Preben Alsholm 

thanks , but due to existance of very large (10^(17)) and very small (10^(-25)) numbers in recent my code, if i use numerical method , i must incrases digite number . result of this change cause that dsolve not compute good or very 
time consuming!!!!

@Doug Meade 

i need sufficient require terms that converge is occure.number terms is not issue.

@Preben Alsholm 

thanks ,but i can not apply your comments.please explain more

thanks

@Preben Alsholm 

thanks but i want solve analytically not numerically!!!

send me fourth order finite difference and shooting methed program code.after see this i can help  you...

@Thomas Richard 

in equations  omega is unknown...

@Preben Alsholm 

thanks, but i dont understand well.please more explain

@vv 

this answer is realated to common''no i work on astronomy...''??