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:
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
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