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Let us consider the following delayed differential equation

$\ddot{y}(t) + 2\dot{y}(t) + 4y = 2\dot{u}(t-\theta) + 4u(t-\theta)$

Here, $y$ is the output, $u$ is the input and $\theta$ denotes the time delay.

How can we mathematically prove if this equation is linear or nonlinear using superposition principle ?

ShiS
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    It is linear as the dependent variables appear linearly. Superposition is a result of linearity and not the other way around. –  Oct 12 '20 at 05:40
  • How can we prove the linearity mathematically using superposition principle? – ShiS Oct 12 '20 at 05:48

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