# Incorrect answer given by RSolve

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 RSolve.

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]] /. %]


• even making it more specific, we get a clearly wrong result, eg : RSolve[{y[n + 1] == y[n] + 1 + Sqrt[y[n]], y[0] == 1}, y, n] (I'm pretty sure there is not a closed form solution, but obviously we shouldn't get an incorrect solution) – george2079 Jul 29 '16 at 14:28
• When you crosspost at Community, please have the courtesy to mention that you posted at SE, and vice versa. – J. M. is in limbo Jul 29 '16 at 18:08
• @J.M., I apologise for my mistake. Thanks for pointing out. – bgamlath Jul 29 '16 at 18:17