By checking all that apply, classify the following differential equation:

$$\displaystyle{\frac{d^3y}{dx^3} y \frac{d^2y}{dx^2} = 0}$$

By checking all that apply, classify the following differential equation:

$$\displaystyle{\frac{1}{\xi^2}\frac{d}{d\xi} \left(\xi^2 \frac{d\psi}{d\xi}\right) = e^{-\psi}}$$

By checking all that apply, classify the following differential equation:

$$\displaystyle{\frac{\partial u}{\partial t} u \frac{\partial u}{\partial x} = \nu \frac{\partial^2u}{\partial x^2}}$$

By checking all that apply, classify the following differential equation:

$$\displaystyle{a\frac{d^2x}{dt^2} b\frac{dx}{dt} cx = 0}$$

By checking all that apply, classify the following differential equation:

$$\displaystyle{\frac{\partial^2 u}{\partial t^2} = c^2\left(\frac{\partial^2u}{\partial x^2} \frac{\partial^2u}{\partial y^2} \frac{\partial^2u}{\partial z^2}\right)}$$