Needs["SpecialFunctions`"]

DE = F'[x] - F[x] == 0

RE = DEtoRE[DE, F[x], a[k]]

REtoDE[RE, a[k], F[x]]

DEtoRE[HolonomicDE[(((ArcSin[(Sqrt[x])]/(Sqrt[x])))^2), F[x]], F[x], 
      a[k]]