@Mariusz Iwaniuk, @tomleslie, @acer thank you very much for your detailed and helpful answers!  :) 

@acer, yes, I see the numerical solution in graphical form, but how do I get it in polynomial form (as in the Python galerkin method)?

http://fredrik-j.blogspot.com/2009/02/galerkins-method-in-sympy.html

result:

1 + 3*x
              2
    8*x   10*x
1 + --- + -----
     11     11
               2       3
    30*x   45*x    35*x
1 + ---- + ----- + -----
     29     116     116
                  2        3        4
    1704*x   882*x    224*x    126*x
1 + ------ + ------ + ------ + ------
     1709     1709     1709     1709
                     2         3         4        5
    31745*x   15820*x    5460*x    1050*x    462*x
1 + ------- + -------- + ------- + ------- + ------
     31739     31739      31739     31739    31739

Is there a function in Maple that can give an numerically result depending on the number of basis functions? Is it possible to solve ode in an analytical (not graphic) way using the built-in Maple tools?

@Mariusz Iwaniuk, thank you very much for your quick and helpful answer!

 I'm new in Maple. Maybe there are approximate methods of solution? Some kind of built-in collocation methods, least squares method, Galerkin method? 

(Something like galerkin in sympy : http://fredrik-j.blogspot.com/2009/02/galerkins-method-in-sympy.html )