The general nonhomogeneous equation is

(1) 
The homogeneous equation is

(2) 

(3) 
Now attempt to convert the equation from

(4) 
to one with constant Coefficients

(5) 
by using the standard transformation for linear SecondOrder Ordinary Differential Equations. Comparing (3) and (5), the functions and are

(6) 

(7) 
Let and define
Then is given by
which is a constant. Therefore, the equation becomes a secondorder ODE with constant Coefficients

(10) 
Define
and
The solutions are
In terms of the original variable ,
© 19969 Eric W. Weisstein
19990525