Question

(D^2-7DD'+6D'^2)Z=0

Answer 1

Given $(D^2-7DD'+6D'^2)z = 0$

Let D' = 1, then auxiliary equation will be,

$m^2-7m+6 = 0 \implies (m-1)(m-6) = 0$

$m = 1,6$

Then general solution of the equation will be,

$z = f(y+x)+g(y+6x)$