Partial Differential Equations

A partial differential equation is given below. $\frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial y^2} = 0$ Possible solution(s) is/are:

Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:

A partial differential equation $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$ is defined for the two-dimensional field $T: T(x, y)$, inside a planar square domain of size 2 m x 2 m. Three bo...

For the following partial differential equation, $x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$ which of the following option(s) is/are CORRECT?

The solution at x = 1, t = 1 of the partial differential equation $\frac{\partial^2 u}{\partial x^2} = 25 \frac{\partial^2 u}{\partial t^2}$ subject to initial conditions of $u(0) = 3x$ and $\frac{\partial u}{\partial t}...