Constructing a differential equation from the solution

[Baumer8993]

Homework Statement

y = c₁e^3x+c₂xe^3x+c₃e^2xsin(x)+c₄e^2xcos(x)

Homework Equations

Differential Equations.

The Attempt at a Solution

I have the roots of k=3, k=3, k=2+i, k=2-i.
Now I am just stuck on how to put the roots together to get the original equation. I am just stuck on the complex number part.

 

[ehild]

What equation is it which has the roots 3, 3, 2+i and 2-i? How do you get such equation from the differential equation? How the powers of k and the degree of the derivatives are related?

ehild