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 ?