Hi, I have the equation y''+100y = 0.5cos(10t) and I have to find the general solution and the IVP.

For the general solution I made the y's into s's and figured out s^2 + 100 = 0 so S 1 & 2 = 0 +/- 10i

From here I found the y-homogeneous part = k1(cos(10t))+k2(sin(10t))

so y-particular = Acos(10t), and I found the second derivitive to equal -100Acos(10t)

The problem is I don't know what to do next. If I plug the A's back in I get -100A+100A = 0.5 and I know this cannot be