d'Alembert's solution of wave equation

[pdestud]

Find the solution of

[MATH] \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} \qquad (t \geq 0, -\infty < x < \infty) [/MATH]
[MATH] u(x,x) = \phi(x) \qquad (-\infty < x < \infty) [/MATH]
[MATH] \frac{\partial u}{\partial x} (x, -x) - \frac{\partial u}{\partial t} (x,-x) = \psi(x) \qquad (-\infty < x < \infty) [/MATH]
where [MATH] \phi(x) [/MATH] and [MATH] \psi(x) [/MATH] are twice continuously differentiable.

 

[Deleted member 4993]

Find the solution of

[MATH] \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} \qquad (t \geq 0, -\infty < x < \infty) [/MATH]
[MATH] u(x,x) = \phi(x) \qquad (-\infty < x < \infty) [/MATH]
[MATH] \frac{\partial u}{\partial x} (x, -x) - \frac{\partial u}{\partial t} (x,-x) = \psi(x) \qquad (-\infty < x < \infty) [/MATH]
where [MATH] \phi(x) [/MATH] and [MATH] \psi(x) [/MATH] 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/