We find specific information about the possible orders of transcendental solutions of equations of the form
f
(
n
)
+
p
n
−
1
(
z
)
f
(
n
−
1
)
+
⋯
+
p
0
(
z
)
f
=
0
f^{(n)}+p_{n-1}(z)f^{(n-1)}+\cdots +p_{0}(z)f=0
, where
p
0
(
z
)
,
p
1
(
z
)
,
…
,
p
n
−
1
(
z
)
p_0(z), p_1(z),\dots , p_{n-1}(z)
are polynomials with
p
0
(
z
)
≢
0
p_0(z) \not \equiv 0
. Several examples are given.