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)
