1) x'' + 2500x = 30 cos 45t where x(0) = 0; x''(0) = 0

i worked it out as y = 0.03sin45t - 0.036 cos 45t.

Yh = 0 and Yp = 0.03sin45t - 0.036 cos 45t.

can anyone confirm this?

2) x'' + 2x' + 26x = 82 cos 4t; x(0) = xa; x'(0) = 0

for xa = 20; 0; 20

somehow i worked it out as Yh = e^-t(cos5t) + (1/5)(e^-t(xa)(sin5t)

Yp = (8/(-8+10i))cos4t + (8/(10+8i))sin4t

i dun think it's right.

really appreciate it if u guys can help. thanks!