Answer
False
Work Step by Step
Since, $z^{\prime\prime}-4z^{\prime}+29z=xe^{x(2+5i)}$
The roots of the auxiliary equation are: $2+5i,2-5i$
So, the correct trial solution must be:
$y_p=A_0x^2e^{(2+3i)x}+B_0xe^{(2+3i)x}$
Therefore, the given statement is $\bf{False}$.
