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solve twice differentiable function

ianchenmu

Member
Feb 3, 2013
74
Let $u:\mathbb{R}^n\rightarrow \mathbb{R}$ be a twice differentiable function. The 2-dimensional wave equation is
$\frac{\partial ^2u}{\partial x^2}=\frac{\partial ^2u}{\partial t^2}$, where $(x,t)$ are coordinates on $\mathbb{R}^2$. Prove that if $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are twice di erentiable functions, then $u(x,t) = f(x-t) + g(x+t)$ solves the 2-dimensional wave equation. Use this fact, or another, to solve the Boundary-Value problem where
$u(s,0) = sin(s) + cos(s)$ , $u(0,s) = -sin(s) + cos(s)$ , $\forall s\in \mathbb{R}$.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Our helpers will really have no idea where you need help when you simply post a problem with no work shown.

I have messaged you about this, and reminded you in a previous topic that our helpers are not here to do the problems, but rather to help you do the problem, and when you do not indicate what you have tried, they really cannot effectively help.

Even if you state that you have no idea even how to begin the problem, this at least lets us know something and gives the helpers a place to begin.

Can you post your work so our helpers have somewhere to begin?