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 Schrödinger 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.