Tifa, in case of required solving with help of finite difference methods :

I would try to ask Maple to integrate the eqn. by its powerful

    ApproximateInt

package. And thereafter ask Maple what of difference scheme it applied.

The package is generalised. If you look in Abramowitz and Stegun's Handbook
(of Mathematical Functions: the Numerical Analysis chapter) you see many a
difference scheme to attack integrals.

It depends on the problem (integrand) what to choose. Maple does this for you. 

Tifa,

if you differentiate the eqn. once more (and ask simplify to clean up the result) 
you get a fifth order homogenous diff. eqn. 

Asking Maple's dsolve( lhs( eqn ) ) you directly get a solution.

This is the homogeneous part. The rhs( eqn ) has a number of
exponential and polynomial items. I did not get an answer directly
to dsolve this inhomegenous part also. It might need some
attention. I didn't wait long enough for Maple to finish it.

Zeineb, the difference between sum and Sum is that the latter is not executed.

In reports you could conveniently use this difference, as follows:

               Sum(2^jj, jj = 0 .. 9); % = evalf(%)  

This gives  Sum(2^jj, jj = 0 .. 9) = 1023.