d'Alembert's solution of wave equation

pdestud

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Sep 14, 2019
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Find the solution of

\(\displaystyle \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} \qquad (t \geq 0, -\infty < x < \infty) \)

\(\displaystyle u(x,x) = \phi(x) \qquad (-\infty < x < \infty) \)

\(\displaystyle \frac{\partial u}{\partial x} (x, -x) - \frac{\partial u}{\partial t} (x,-x) = \psi(x) \qquad (-\infty < x < \infty) \)

where \(\displaystyle \phi(x) \) and \(\displaystyle \psi(x) \) are twice continuously differentiable.
 

Subhotosh Khan

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Jun 18, 2007
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Find the solution of

\(\displaystyle \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} \qquad (t \geq 0, -\infty < x < \infty) \)

\(\displaystyle u(x,x) = \phi(x) \qquad (-\infty < x < \infty) \)

\(\displaystyle \frac{\partial u}{\partial x} (x, -x) - \frac{\partial u}{\partial t} (x,-x) = \psi(x) \qquad (-\infty < x < \infty) \)

where \(\displaystyle \phi(x) \) and \(\displaystyle \psi(x) \) are twice continuously differentiable.
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How is this problem different from the "almost" duplicate problem you posted at:

https://www.freemathhelp.com/forum/threads/dalembert-formula.118383/
 
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