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Show that the solution of the initial value problem my?? + ?y? + ky = 0, y(t0) = y0, y? (t0) = y1 can be expressed as th

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Show that the solution of the initial value problem my?? + ?y? + ky = 0, y(t0) = y0, y? (t0) = y1 can be expressed as the sum y = ? + w, where ? satisfies the initial conditions ?(t0) = y0, ?? (t0) = 0, w satisfies the initial conditions w(t0) = 0, w? (t0) = y1, and both ? and w satisfy the same differential equation as u. This is another instance of superposing solutions of simpler problems to obtain the solution of a more general problem.

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