Finding a particular integral for differential

d^2y/dx^2 + 9y= 2sin3x

Apparently is -1/3(xcosx) I can't get this

Complementary soln.based on
d^2y/dx^2 + 9y = 0
Subst. y = e^mx leads to
m^2 + 9 = 0
m = +3i or m = -3i
y = Pe^3ix + Qe^-3ix
= P[cos 3x + i sin 3x) + Q[cos 3x - i sin 3x)
with different constants
y = Acos 3x + Bsin 3x

Use method undetermined coefficients
d^2y/dx^2 + 9y = 2sin3x.....(1)
has particular soln, of form
y = x(Acos 3x + Bsin 3x)......(2)
(Refer to guide to particular solution forms)
Substitute 2 into 1 and simplify
6Bcos 3x - 6asin 3x = 2sin 3x
Equating coefficients B= 0, A = (-1/3)
Particular soln y = (-x/3)cos 3x

General soln.
y = (-x/3)cos 3x + Rcos 3x + Tsin 3x

Regards - Ian

yp = x[asin(3x) + bcos(3x)] , find y " and plug to d^2y/dx^2 + 9y= 2sin3x, and solve for a , b