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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