Engineering Mathematics - Partial Differential Equations

Consider the following expression: $z = \sin(y+it)+\cos(y-it)$ where z, y, and t are variables, and $i=\sqrt{-1}$ is a complex number. The partial differential equation derived from the above expression is

The function $f(x, y)$ satisfies the Laplace equation $\nabla^2 f(x, y) = 0$ on a circular domain of radius $r = 1$ with its center at point $P$ with coordinates $x = 0, y = 0$. The value of this function on the circular...

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} + \frac{\partial K(\theta)}{\partial z} - \...