$\displaystyle y''+y=7sin(2t)+5tcos(2t)$

Since g(t) is a sum I'll have 2 equations.

$\displaystyle y''+y=7sin(2t)$

$\displaystyle y''+y=5tcos(2t)$

I'm kind of confused on which forms of Y to use.

Would $\displaystyle Y_1 (t)=Asint(2t)$ and $\displaystyle Y_2 (t)=(At+B)sin(2t)+(At+B)cos(2t)$ ?