What is the General Solution for a Differential Equation with Complex Roots?

[jbord39]

Homework Statement

(D^2 + 2D + 10)^2 * (D^2 - 2D -3)y = 0.

Homework Equations

D = d/dx

The Attempt at a Solution

Solving for the roots gives:

-1 + 3i, -1 - 3i <== both of multiplicity 2
and 3, -1.

So the general solution should be:

y = Ae^(3x) + Be^(-x) + Ce^(-x)cos(3x) + Dxe^(-x)cos(3x) + Ee^(-x)sin(3x) + Fxe^(-x)sin(3x)

Am I handling this correctly?

Thanks

 

[Dick]

Looks ok to me.

 

[jbord39]

Thanks for looking at it.