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

Prove that for an nth order differential equation whose auxiliary equation has a repeated complex root a+bi of multiplicity k then its conjugate is also a root of multiplicity k and that the general solution of the corresponding differential equation contains a linear combination of the 2k linearly independent solutions

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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Expert Solution

Colby Messinger answered 1 year ago

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