Given y prime equals 1/2 equals 5 times cosine of 2t, find the solution of this initial value problem and describe its behavior for large t.

a) y of t equals 10 times sine of 2t plus C, where C is a constant
b) y of t equals 10 times cosine of 2t plus C, where C is a constant
c) y of t equals 5 times sine of 2t plus C, where C is a constant
d) y of t equals 5 times cosine of 2t plus C, where C is a constant