Maybe this helps a little:
Internal`InheritedBlock[{Solve}, Unprotect[Solve];
Solve[x___] :=
Block[{$guard = True}, Print["Solve called : ", HoldForm[Solve[x]]];
Solve[x]] /; ! TrueQ[$guard];
DSolve[{-x^2 + (0.232866 - 0.232166*Cos[y[x]])*y'[x]^2 == 0}, y[x], x]];
(*Solve called : Solve[10 Sqrt[14] EllipticE[y[x]/2,-(116083/175)]==-((5714200963 x^2)/16162201)+Subscript[\[ConstantC], 1],y[x]]*)
We see that solution is implicit form:
10 Sqrt[14] EllipticE[y[x]/2,-(116083/175)]==-((5714200963 x^2)/16162201)+C[1]
where: C[1] is a integration constant.
For: EllipticE
,#
and &
see in Documentation Center