Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later
Also posted in Wolfram Community.
I tried to solve the following nonlinear recurrence relation using
y[n+1] = y[n] - a - b Sqrt[y[n]]
But the solution given by
RSolve does not satisfy the relation.
Have I missed anything regarding RSolve or is this a bug in Mathematica?
Code is given below.
RSolve[y[n + 1] == y[n] - a - b Sqrt[y[n]], y, n] FullSimplify[y[n + 1] == y[n] - a - b Sqrt[y[n]] /. %]