Looks like you've accidentaly assigned a value to Derivative:

(* How the y''[x] expression looks without nice syntax: *)

y''[x]//FullForm

(* Derivative[2][y][x] *)

DSolve[{y''[x] == y[x]}, y[x], x]

(* {{y[x] -> E^x C[1] + E^-x C[2]}} *)

y''[x] = whoops

D[y[x], {x, 2}]

(* whoops *)

whoops = y[x]

D[y[x], {x,2}]

(* y[x] *)

(* Let's try to fix it by clearing y *)

ClearAll[y];

D[y[x], {x,2}]

(* y[x] didn't work *)

(* Clear the strange definition by: *)

y''[x]=.

D[y[x], {x,2}]

(* y''[x] *)

What goes wrong is the assignment to y'' which is easier to understand by remembering the FullForm:

Derivative[2][y][x] = something

making all kinds of strange things happen.