I need help with the following problem:

y'' + 4y = cos^2(t)

Here is what I have done so far

y'' + 4y = (1/2) + (1/2)cos(2t) (power reduction formula)

Y(t) = A + B*sin(2t) + C*cos(2t)

Y'(t) = 2B*cos(2t) - 2C*sin(2t)

Y''(t) = -4B*sin(2t) - 4C*cos(2t)

Pluging in Y(t) and Y''(T) into the original equation, I get:

[-4B*sin(2t) - 4C*cos(2t)] + 4[A + B*sin(2t) + C*cos(2t)] = (1/2) + (1/2)cos(2t)

4A = (1/2) + (1/2)cos(2t)

As you can see, the B and C terms cancel each other out, leaving only an A term. What should I do from here? Is there anything I did wrong?