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Derive the linearized disturbance equation for the next PDE du dt du + u + Cu = 0 dx where C is a constant.

Derive the linearized disturbance equation for the next PDE du dt du + u + Cu = 0 dx where C is a constant. Assume that up is the known base solution, satisfying the same equation. Plug in a waveform solution u(x, t) = dcos (kx - wt) and simplify the resulting equation.

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