$\displaystyle y^{\prime \prime} + 81 y = 9 \sin(9 x) + 9 + e^{9 x}$

My Yp expression is:

$\displaystyle

C_{1}x\cos(9 x) + C_{2} x\sin(9 x) + C_{3} + C_{4}e^{9 x}

$

But for this one,

$\displaystyle y^{\prime \prime} - 25 y = 5 \cos(5 x) + 5 + e^{5 x}$

its:

$\displaystyle C_{1}\cos(5 x) + C_{2} \sin(5 x) + C_{3} + C_{4}x e^{5 x}$

For the second one, the expression for cos(5x) is written as [tex]$\displaystyle C_{1}\cos(5 x) + C_{2} \sin(5 x)$

but for the first one, sin(9x) its :

$\displaystyle

C_{1}x\cos(9 x) + C_{2} x\sin(9 x)

$

Why does the second instance have an x infront of the cos and sin? Whats the rule here?