Use  in your derivation.

You should be able to derive the following equation of motion:
 ….. (*)
Now, let  be a solution of the above equation.

Try to obtain the following by successive differentiation: 
  and

Substitute those expressions of x,  and  into equation (*), you should be able to get the following equation after simplification:

As L.H.S. is identical to zero for all t, 

From (1), .
From (2),
	(Note that: )

i.e. 

which represents a periodic motion with amplitude Ae-t, and angular frequency 
.