In 13?18, find the solution to the initial value problem.
Chapter 10, Problem 14E(choose chapter or problem)
In Problems , find the solution to the initial value problem.
\(\frac{\partial^{2} u}{\partial t^{2}}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}}, \quad-\infty<x<\infty, \quad t>0\)
\(u(x, 0)=f(x), \quad-\infty<x<\infty\)
\(\frac{\partial u}{\partial t}(x, 0)=g(x),-\infty<x<\infty\)
for the given functions \(f(x) \text { and } g(x)\)
\(f(x)=x^{2}, g(x)=0\)
Equation Transcription:
Text Transcription:
\partial^2 u\partial t^2=\alpha^2 \partial^2 u\partial x^2 \quad-\infty<x<\infty, \quad t>0
u(x, 0)=f(x), \quad-\infty<x<\infty
\partial u\partial t(x, 0)=g(x),-\infty<x<\infty
f(x) and g(x)
f(x)=x^2, g(x)=0
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