Finding the second derivative of a function and adding another function onto it to show that the new function is equal to zero

Question

Say you have a function, f(x) = cos2x + sin2x, you then differentiate it twice to get f ''(x) = -4cos2x - 4sin2x. But how would show that f ''(x) + 4y is equal to zero? I don't really understand what the question means when adding the 4y, could someone also explain this? Thanks.

Answer 1

HINT

We have

• $f(x) = \cos2x + \sin2x$
• $f''(x) = -4 \cos2x -4\sin 2x$

then evaluate $$4f(x)+f''(x)$$