Chapter 4.1, Problem 35E

(a) Verify that $y_{p1}=3e^{2x}$ and $y_{p2}=x^2+3x$are, respectively, particular solutions of

$y"-6y\text{'}+5y=-9e^{2x}$

and $y"-6y\text{'}+5y=5x^2+3x-16$

(b) Use part (a) to find particular solutions of

$y"-6y\text{'}+5y=5x^2+3x-16-9e^{2x}$

and $y"-6y\text{'}+5y=-10x^2-6x+32+e^{2x}$