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Prove that for an nth order differential equation whose auxiliary equation has a repeated complex root...

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Advance Math

Prove that for an nth order differential equation whoseauxiliary equation has a repeated complex root a+bi of multiplicityk then its conjugate is also a root of multiplicity k and that thegeneral solution of the corresponding differential equationcontains a linear combination of the 2k linearly independentsolutions

e^(ax)cos(bx),xe^(ax)cos(bx),  x^2e^(ax)cos(bx),...,  x^(k-1)e^(ax)cos(bx)

e^(ax)sin(bx), xe^(ax)sin(bx), x^2e^(ax)sin(bx),...,x^(k-1)e^(ax)sin(bx)

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