rsolve not giving full solution to 2nd order difference equation

[Kaloyan Ganev]

Hi there,

I am trying to solve a simple 2nd order difference equation using rsolve (for demonstration purposes). This is my code:

from sympy import Function, rsolve
from sympy.abc import n
y = Function('y')

f = y(n + 2) - 4.75*y(n + 1) + 4*y(n) - 150

sol2 = rsolve(f, y(n))
print(sol2)

The solution that is reported is not the full one but only: 3.65586884574495**n*C0 + 600.0, i.e. the larger root is taken into account only, and the particular solution.

When I run the following, things are getting OK (but not quite, because every time you have to guess the appropriate integers for your fraction):

from fractions import Fraction
from sympy import Function, rsolve
from sympy.abc import n
y = Function('y')

f = y(n + 2) - Fraction(19,4)*y(n + 1) + Fraction(4,1)*y(n) - 150

sol = rsolve(f, y(n))
print(sol)

The solution now is as expected: C0*(-sqrt(105)/8 + 19/8)**n + C1*(sqrt(105)/8 + 19/8)**n + 600

What could I be doing wrong in my first example?