Suppose that a fourth order differential equation has a solution .

(a) Find such a differential equation, assuming it is homogeneous and has constant coefficients.
help (equations)
Note: for part (a), use primes to denote derivatives.

(b) Find the general solution to this differential equation. In your answer, use and to denote arbitrary constants and the independent variable.
help (equations)
Note: for this part, you MUST enter before your answer. For example, if I thought the answer was I would literally enter .

Question

Suppose that a fourth order differential equation has a solution . 

(a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. 
 help (equations) 
Note: for part (a), use primes to denote derivatives. 

(b) Find the general solution to this differential equation. In your answer, use  and  to denote arbitrary constants and  the independent variable. 
 help (equations) 
Note: for this part, you MUST enter  before your answer. For example, if I thought the answer was  I would literally enter .