can i have the answer of the desolve after the singular ponit ? so that i can find what happens in the singular point? and also can i know number of singular points ?

can i have the answer of the desolve after the singular ponit ? so that i can find what happens in the singular point? and also can i know number of singular points ?

what is the relation governing to P(i)s? if u say the relation,i think it is to easy to find the sum .

@rlopez thank u afterall, for your help and attention, as u said,Preben Alsholm always helps us with detailed answers and i am really thankful for his good help and good ideas,god bless u and him.thank u.

thank u for your discussion in here,and for your attention,
my problem is modeling a physical system and a real one,and if i change the initial conditions of the system,the parameters would change and maybe will be as u said,rescaled. but if i do that,my problem loses its physical face and changes to pure math which is not my aim to discuss.
setting some parameters to 0 is sth that can be invistageted, but i do not know what u mean by setting exponents to zero ? which exponents? 
but this kind of approach is perfect as for finding the problem with the equations,and thus i am really thankful for your idea for solving the problem.thank u.

thank u for your discussion in here,and for your attention,
my problem is modeling a physical system and a real one,and if i change the initial conditions of the system,the parameters would change and maybe will be as u said,rescaled. but if i do that,my problem loses its physical face and changes to pure math which is not my aim to discuss.
setting some parameters to 0 is sth that can be invistageted, but i do not know what u mean by setting exponents to zero ? which exponents? 
but this kind of approach is perfect as for finding the problem with the equations,and thus i am really thankful for your idea for solving the problem.thank u.

thanks for your detailed answer, i have another question ? why u said it is unwise to change the float point to 3 ? and what did u mean by keep theiir signs?
 i have another idea to say, maple solvers approximately awared me of the sort of the singular point since non of them does not solve the problem further, but i used step by step time integration method,and it does answered the problem, and my results  matched well with a CAE software. i actually do not know why this happens with maple solvers,and if it is a real singular one,why the other method solve it?

thanks for your detailed answer, i have another question ? why u said it is unwise to change the float point to 3 ? and what did u mean by keep theiir signs?
 i have another idea to say, maple solvers approximately awared me of the sort of the singular point since non of them does not solve the problem further, but i used step by step time integration method,and it does answered the problem, and my results  matched well with a CAE software. i actually do not know why this happens with maple solvers,and if it is a real singular one,why the other method solve it?

thanks for the answer,but my ode include the coefficients of one function, not the function itself,so i just need to use them and multiply them by x so that i can plot the function,and i could not do that with ode plot. thanks anyway.

thanks for the answer,but my ode include the coefficients of one function, not the function itself,so i just need to use them and multiply them by x so that i can plot the function,and i could not do that with ode plot. thanks anyway.

@jschulzb u are right.

@jschulzb u are right.

@Markiyan Hirnyk i think the answer is no since we define :
declare(y(x), prime=x):
here x is the primary variable ,y is the function of x,so its derivatives are also function of x,and i do not think x is the function of y'(x) since it is the priamary variable,evenif we can solve x with respect to y and y'(x),but it does not change the main issue,x IS the primary variable,and thus is independet of anything ,

@Markiyan Hirnyk i think the answer is no since we define :
declare(y(x), prime=x):
here x is the primary variable ,y is the function of x,so its derivatives are also function of x,and i do not think x is the function of y'(x) since it is the priamary variable,evenif we can solve x with respect to y and y'(x),but it does not change the main issue,x IS the primary variable,and thus is independet of anything ,

thanks alot,that's exactly what i needed.