linearity

In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ $D(\theta)\frac{\partial^2\theta}{\partial z^2} + \...

The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is

The differential equation $${{{d^4}y} \over {d{x^4}}} + P{{{d^2}y} \over {d{x^2}}} + ky = 0\,\,$$ is