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Math Help - Linear ODE with const. coeff for a fundamental solution set

  1. #1
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    Linear ODE with const. coeff for a fundamental solution set

    For the fundamental solution set S={ex,e2x,e3x} 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
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  2. #2
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    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: r3 - 6r2 + 11r - 6 = 0

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

    Could anyone please confirm if this method is correct?
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