Section: Engineering Mathematics | Marks: 2
Linked Answer Q.27 & Q.28: The potential $u(x,y)$ satisfies the equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ in the square $0 \le x \le \pi$, $0 \le y \le \pi$. Three of the edges $x = 0$, $x = \pi$ and $y = 0$ of the square are kept at zero potential and the edge $y = \pi$ is kept at nonzero potential. The potential $u(x,y)$ is given by
- A. $u(x,y) = \sum_{n=1}^\infty A_n \cosh nx \sin ny$
- B. $u(x,y) = \sum_{n=1}^\infty A_n \sin nx \cosh ny$
- C. $u(x,y) = \sum_{n=1}^\infty A_n \sinh nx \sin ny$
- D. $u(x,y) = \sum_{n=1}^\infty A_n \sin nx \sinh ny$