The problem of solving equations in groups can be stated as follows: given a group
G
G
and a free group
F
=
F
(
x
1
,
x
2
,
…
)
F = F\left ( {{x_1},{x_2}, \ldots } \right )
, for which pairs
(
w
,
g
)
\left ( {w,g} \right )
with
w
=
w
(
x
1
,
x
2
,
…
)
∈
F
,
g
∈
G
w = w\left ( {{x_1},{x_2}, \ldots } \right ) \in F,g \in G
, is it possible to find elements
g
i
∈
G
{g_i} \in G
such that
w
(
g
1
,
g
2
,
…
)
=
g
w\left ( {{g_1},{g_2}, \ldots } \right ) = g
? We investigate the corresponding question of solving equations in the group
A
(
Ω
)
A\left ( \Omega \right )
of all automorphisms of a transitive tree
Ω
\Omega
. If the tree has isomorphic cones at a branch point, then certain equations of the form
x
n
=
g
{x^n} = g
cannot be solved (Theorem 2.3). If the tree is sufficiently transitive, we find large classes of equations
w
=
g
w = g
which can be solved (Theorems 2.13, 2.16).