(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider an electrical cable running along the x-axis which is not well insulated from ground, so that leakage occurs along its entire length. Let V(x,t) and I(x,t) denote the voltage and current at point x in the wire at time t. These functions are related to each other by the system

[tex]\frac{\partial V}{\partial x}=-L \ \frac{\partial I}{\partial t}- RI, \ and \ \frac{\partial I}{\partial x}=-C\\\frac{\partial V}{\partial t}-GV[/tex]

where L is the inductance, R is the resistance, C is the capacitance, and G is the leakage to ground. Show that V and I each satisfy

[tex]\frac{\partial^{2}u }{\partial x^{2}}=LC\frac{\partial^{2} u }{\partial t^{2}}+(RC+LG)\frac{\partial u }{\partial t}+RGu [/tex]

which is called thetelegraph equation.

2. Relevant equations

3. The attempt at a solution

I am not sure of even where to start. Initially I would think a change in variable might do it, but then again, I don't know what change in variable to use. Any suggested course of action?

Thanks.

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# Homework Help: Another PDE question Where do I begin?

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