  In this paper, we consider the charged non-extremal black hole at five
dimensional N = 2 supergravity. We study thermodynamics of AdS_{5} black hole
with three equal charges (q_{1} = q_{2} = q_{3} = q). We obtain Schrodinger
like equation and discuss the effective potential. Then, we consider the case
of the perturbed dilaton field background and find presence of odd coefficients
of the wave function. Also we find that the higher derivative corrections have
no effect on the first and second even coefficients of the wave function.
