In 1–5, find a formal solution to the given boundary value

Chapter 10, Problem 3E

(choose chapter or problem)

In Problems 1-5, find a formal solution to the given boundary value problem.

$\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0, \quad 0<x<\pi, \quad 0<y<\pi$

$u(0, y)=u(\pi, y)=0, \quad 0 \leq y \leq \pi$

$u(x, 0)=f(x), \quad 0 \leq x \leq \pi$

$u(x, \pi)=0, \quad 0 \leq x \leq \pi$

Equation Transcription:

$\frac{{\partial{}}^{2}u}{\partial{}{x}^{2}}+\frac{{\partial{}}^{2}u}{\partial{}{y}^{2}}=0,\ \ \ 0<x<\pi{},\ \ \ 0<y<\pi{}$

$u(0,y)=u(\pi{},y)=0,\ \ 0\leq{}y\leq{}\pi{}$

$u(x,0)=f(x),\ \ \ \ 0\leq{}x\leq{}\pi{}$

$u(x,\pi{})=0,\ \ \ \ \ \ \ \ \ 0\leq{}x\leq{}\pi{}$

Text Transcription:

partial^2 u\partial x^2+\partial^2 u\partial y^2=0, \quad 0<x<\pi, \quad 0<y<\pi

u(0, y)=u(\pi, y)=0, \quad 0 \leq y \leq \pi

u(x, 0)=f(x), \quad 0 \leq x \leq \pi

u(x, \pi)=0, \quad 0 \leq x \leq \pi

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Login