prove that for an nth order ordinary differential equation with constant coefficients whose characteristic polynomial has...

 

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prove that for an nth order ordinary differential equation with constant coefficients whose characteristic polynomial has a repeated root r of multiplicity m then that equation will have linearly independent solutions of the form et, te^t, t^2e^t, t^3e^t, ..., t^(m-1)e^t prove that for an nth order ordinary differential equation with constant coefficients whose characteristic polynomial has a repeated root r of multiplicity m then that equation will have linearly independent solutions of the form et, te^t, t^2e^t, t^3e^t, ..., t^(m-1)e^t