Chapter 1, Problem 5RE

(a)

To determine

Whether the differential equation $\frac{\partial \varphi }{\partial x}\left(\frac{{\partial }^2\varphi }{\partial x^2}\right)=\frac{{\partial }^2\varphi }{\partial y^2}$ is an ordinary differential or a partial differential equation.

(b)

To determine

The order of the differential equation $\frac{\partial \varphi }{\partial x}\left(\frac{{\partial }^2\varphi }{\partial x^2}\right)=\frac{{\partial }^2\varphi }{\partial y^2}$.

(c)

To determine

Whether the differential equation $\frac{\partial \varphi }{\partial x}\left(\frac{{\partial }^2\varphi }{\partial x^2}\right)=\frac{{\partial }^2\varphi }{\partial y^2}$ is linear or non-linear.