An investigation is made of the differential equation
\[
d
2
w
/
d
x
2
=
{
u
2
(
x
−
x
0
)
λ
f
(
u
,
x
)
+
g
(
u
,
x
)
/
(
x
−
x
0
)
2
}
w
,
{d^2}w/d{x^2} = \{ {u^2}{(x - {x_0})^\lambda }f(u,x) + g(u,x)/{(x - {x_0})^2}\} w,
\]
in which u is a large real (or complex) parameter,
λ
\lambda
is a real constant such that
λ
>
−
2
\lambda > -2
, x is a real (or complex) variable, and
f
(
u
,
x
)
f(u,x)
and
g
(
u
,
x
)
g(u,x)
are continuous (or analytic) functions of x in a real interval (or complex domain) containing
x
0
{x_0}
. The interval (or domain) need not be bounded. Previous results of Langer and Riekstins giving approximate solutions in terms of Bessel functions of order
1
/
(
λ
+
2
)
1/(\lambda + 2)
are extended and error bounds supplied.