Maxima Function
funcsolve (eqn, g(t))
Returns [g(t) = ...]
or []
, depending on whether
or not there exists a rational function g(t)
satisfying eqn,
which must be a first order, linear polynomial in (for this case)
g(t)
and g(t+1)
(%i1) eqn: (n + 1)*f(n) - (n + 3)*f(n + 1)/(n + 1) = (n - 1)/(n + 2); (n + 3) f(n + 1) n - 1 (%o1) (n + 1) f(n) - ---------------- = ----- n + 1 n + 2 (%i2) funcsolve (eqn, f(n)); Dependent equations eliminated: (4 3) n (%o2) f(n) = --------------- (n + 1) (n + 2)
Warning: this is a very rudimentary implementation -- many safety checks and obvious generalizations are missing.