@Carl Love 

can you create a worksheet ?

thanks

@Carl Love 

well i know this equation has no solution : eqqq.mw

but  for another equation maple gave one solution but i obtained two solutions handy !

eq0.mw  

maybe the first equation has solution but maple didnt result them

@Axel Vogt 

i have this one and want to know  what values of a , phi[0] , n  and c satisfies this equation.

well what is name of the equations like this ?  ......... parametric ?      

Download eqqq.mw

thanks guys

@Carl Love 

for w^0 , is it correct ?

coeff(ex,w,0)/w^0+coeff(ex, w, -1)/w + coeff(ex, w, -2)/w^2;

-1 or -2 in above what it means ?

and another question , i want to write original equation without any factoring 

best regards

dear @acer, i want to have this long term without any factoring . 

@acer 

nothing happens JJ.mw

@tomleslie 

clear.mw

@tomleslie 

yep i didn't mean alpha(r)=alpha_0+alpha_1*r+alpha_2*r^2 or alpha(r)=alpha_0+alpha_1/r+alpha_2/r^2.

in fact i have 4 set of differential equations which this is one of them and because there is no exact solutions for them , i want to use perturbation method for solving them. for this purpose , alpha(r) expands as power series with parameter 1/w (w is big) which assume alpha_0(r) is constant.