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 11
 Problem Statement
 given the one dimensional wave equation and the two variables E and n, solve for:
 Relevant Equations

$$\frac{\partial^2 u}{\partial t^2}  c^2\frac{\partial^2 u}{\partial x^2} = 0$$
E = x + ct
n = x  ct
I am given the following:
$$u = (x,t)$$
$$\frac{\partial^2 u}{\partial t^2}  c^2\frac{\partial^2 u}{\partial x^2} = 0$$
and
$$E = x + ct$$
$$n = x  ct$$
I need to solve for $$\frac{\partial^2 u}{\partial x^2}$$ and $$\frac{\partial^2 u}{\partial t^2}$$
using the chain rule.How would I even begin? Would I have to say that:
$$ x = (E, t)$$
$$ x =(n, t)$$
thus
$$u(x,t) = u( x(E,t) , t)$$
and
$$ u(x,t) = u(x(n,t),t)$$?
$$u = (x,t)$$
$$\frac{\partial^2 u}{\partial t^2}  c^2\frac{\partial^2 u}{\partial x^2} = 0$$
and
$$E = x + ct$$
$$n = x  ct$$
I need to solve for $$\frac{\partial^2 u}{\partial x^2}$$ and $$\frac{\partial^2 u}{\partial t^2}$$
using the chain rule.How would I even begin? Would I have to say that:
$$ x = (E, t)$$
$$ x =(n, t)$$
thus
$$u(x,t) = u( x(E,t) , t)$$
and
$$ u(x,t) = u(x(n,t),t)$$?