We know that if

$y_p=u_1(t)+e^{\frac{t}{3}}{u}_2(t)+e^{-\frac{t}{3}}{u}_3(t)$

is a particular solution of the differential equation $9y^{\text{'}\text{'}\text{'}}-y^{\text{'}}=g(t),$ then

$u_1^{\text{'}}=\frac{g(t)W_1(t)}{W(t)}.,$ Find $W_1(t)$

Select one:

$-\frac{2}{3}$

$\frac{1}{3}{e}^{\frac{t}{3}}$

none of the given answers is true

$\frac{1}{3}{e}^{-\frac{t}{3}}$

$\frac{2}{3}$