undetermined coefficients in DE given y"+4y'=16x find a general solution through undetermined coefficients. I have found yc to be yc = c1 + c2e^(-x) and I have chosen yp to be yp = ax^2 + bx Just wondering if this yp is a good choice

Your complementary functions contains a constant $c_1$, so you are correct in multiply the "usual/default" particular integral $y_{p_o} = ax + b$ by $x$ to get $y_p = ax^2 + bx$.