thanks for your answer Mr. Fantastic...ill show ya what i did cuz i have a mistake and i don't know where it is...so let's see:

first of all i took the first solution and i evaluated it in the equation and yes it was a solution (i had already done it before but i didn't do it well)

so then i did grade reduction to get the second solution which in the exercise said it had to be:

well so this is what i got:

where v(x) is my unknown solution

then replacing on the diff eq. (which was

with N>0)

some sums and products later...

Mr F says: I think you'll find this should be . And you can divide out the common factor of e^x.
then i suppouse that

so the new equation is:

which is a separable diff. equation

here is the problem i think...

(while i was writing this i noticed my mistake, i was not ok because i put

let's c if i'm right...)

remember that u=v' so:

and finally:

but i`m still missing the minus where do i get it (omg it worked pretty good)

and the other point i care is that i gotta prove that this second solution is a polynomial of N grade...