Question $6$

What would $be$ a good guess function for the particular

solution?

$3x^{\text{'}\text{'}}+4x^{\text{'}}+5x=3t^2{e}^{3t}$

Choose one answer only:

$(a)x_p=e^{3t}(A{t}^2+Bt+C)$

$(b)x_p=A{e}^{3t}{t}^2$

$(c)x_p=A{e}^{3t}$

$(a)$

$(b)$

$(c)$