Question

(D+D'-2)Z = 0

Answer 1

Corresponding for each non-repeated factor (bD-aD'-c) general solution is taken as

$e^{cx/b}\phi(ax+by), b \not=0$

$D+D'-2=e^{2x}\phi_1(x-y)$

Answer: $z=e^{2x}\phi_1(x-y)$