The Ermakov equation, also called the Ermakov-Pinney equation, is the nonlinear second-order ordinary differential equation
 |
where 
is a nonzero constant. If 
and 
are linearly independent
solutions of the associated linear differential
equation 
,
then solutions can be written
 |
where 
,
, 
, and 
are constants, 
, and 
is the constant Wronskian
of 
and 
.
The expression applies on intervals where the radicand
is positive.
." Proc.
Amer. Math. Soc. 1, 681, 1950.