Linear ODE with const. coeff for a fundamental solution set

For the fundamental solution set **S={e**^{x},e^{2x},e^{3x}} can we construct a linear ODE with constant coefficients?

I have verified that the solution set is linearly independent via wronskian. I have got the annihilators as (D-1),(D-2),(D-3). However after that I'm not sure how to proceed. What do I do to get the ODE?

Thanks

Re: Linear ODE with const. coeff for a fundamental solution set

I have progressed a little more:

From the annihilators, I get the characteristic equation to be: r^{3} - 6r^{2} + 11r - 6 = 0

Which gives me the linear ODE: y''' - 6y'' + 11y' - 6 = 0

Could anyone please confirm if this method is correct?