Needs["SpecialFunctions`"]

HolonomicDE[(Sqrt[1 + x]) + (1/(Sqrt[1 + x])), F[x]]

HolonomicDE[A (Sqrt[ 1 + x]) + (B/(Sqrt[1 + x])), F[x]]

HolonomicDE[Simplify[(Sqrt[1 + x]) + (1/(Sqrt[1 + x]))], F[x]]

holonomicDE[(Sqrt[1 + x]) + (1/(Sqrt[1 + x])), F[x]]

(Subscript[DE, 1]) = HolonomicDE[(Sqrt[1 + x]), F[x]]

(Subscript[DE, 2]) = HolonomicDE[(1/(Sqrt[1 + x])), F[x]]

SumDE[(Subscript[DE, 1]), (Subscript[DE, 2]), F[x]]

Simplify[(Sqrt[1 + x]) + (1/(Sqrt[1 + x]))]

(Subscript[DE, 3]) = HolonomicDE[x + 2, F[x]]

ProductDE[(Subscript[DE, 2]), (Subscript[DE, 3]), F[x]]

ProductDE[F'[x] - F[x] == 0, F''[x] +  F[x] == 0, 
      F[x]]

HolonomicDE[(E^x)*Sin[x], F[x]]

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

DSolve[{DE, F[0] == 1}, F[x], x]