In 13?18, find the solution to the initial value problem.
Chapter 10, Problem 13E(choose chapter or problem)
In Problems 13-18, find the solution to the initial value problem.
\(\frac{\partial^{2} u}{\partial t^{2}}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}}, \quad-\infty<x<\infty, \quad t>0\),
\(u(x, 0)=f(x), \quad-\infty<x<\infty\),
\(\frac{\partial u}{\partial t}(x, 0)=g(x), \quad-\infty<x<\infty\)
For the given functions \(f(x)\) and \(g(x)\).
\(f(x) \equiv 0, \quad g(x)=\cos x\)
Equation Transcription:
Text Transcription:
partial^2u/partial t^2=alpha^2 partial^2 u/partial x^2, -infty<x<infty,t>0
u(x,0)=f(x), -infty<x<infty,t>0
Partial u/partial t(x,0)=f(x), -infty<x<infty
f(x)
g(x)
f(x)equiv 0, g(x)cos x
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