Derive a formula for the solution to the following

Chapter 10, Problem 10E

(choose chapter or problem)

Derive a formula for the solution to the following initial-boundary value problem involving nonhomogeneous boundary conditions

$\frac{\partial^{2} u}{\partial t^{2}}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}}, \quad 0<x<L, \quad t>0$

$u(0, t)=U_{1}, \quad u(L, t)=U_{2}, t>0$

$u(x, 0)=f(x), \quad 0<x<L$

$\frac{\partial u}{\partial t}(x, 0)=g(x), \quad 0<x<L$

where $U_{1} \text { and } U_{2}$ are constants.

Equation Transcription:

$\frac{{\partial{}}^{2}u}{\partial{}{t}^{2}}={\alpha{}}^{2}\frac{{\partial{}}^{2}u}{\partial{}{x}^{2}},\ \ 0<x<L,\ \ t>0$

$u(0,t)={U}_{1},\ \ u(L,t)={U}_{2},\ \ t>0$

$u(x,0)=f(x),\ \ 0<x<L$

$\frac{\partial{}u}{\partial{}t}(x,0)=g(x),\ \ 0<x<L$

${U}_{1}\ and\ {U}_{2}$

Text Transcription:

\partial^2 u\partial t^2=\alpha^2\partial^2 u\partial x^2, \quad 0<x<L, \quad t>0

u(0, t)=U_1, \quad u(L, t)=U_{2}, t>0

u(x, 0)=f(x), \quad 0<x<L

\partial u\partial t(x, 0)=g(x), \quad 0<x<L

U_1 and U_2

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