In 1318, find the solution to the initial value problem.

Chapter 10, Problem 17E

(choose chapter or problem)

In Problems 13-18, find the solution to the initial value problem.

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

$u(x,0)=f(x),\quad\ \ -\infty<x<\infty,\quad\ \ t>0$,

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

For the given functions $f(x)$ and $g(x)$.

$f(x)=e^{-x^{2}}, \quad g(x)=\sin x$

Equation Transcription:

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

$u(x,0)=f(x),\ \ -\infty{}<x<\infty{},\ \ \ t>0$

$\frac{\partial{}u}{\partial{}t}(x,0)=f(x),\ \ -\infty{}<x<\infty{}$

$f(x)$

$g(x)$

$f(x)={e}^{-{x}^{2}},\ \ g(x)=sin\ x$

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)=e^-x^2, g(x)=sin x

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