What is the Fault in My Derivation of the Wave Equation in a Conductor?

[Nikitin]

Homework Statement

http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_Dec_2008_tfy4240.pdf
problem 2a)

Homework Equations

The Attempt at a Solution

Hi. In problem 2a I was supposed to find a wave equation, however while digging around in maxwell's equations, I found this result:

https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-xap1/v/t1.0-9/16410_10204393293009062_1155886601331102418_n.jpg?oh=44e1d9886a54e34274c00437ed952ca5&oe=5505B805&__gda__=1427040332_aace122d9214b5db9de482b3e631a490

which effectively implies that $\nabla^2 \vec{E} = 0$ if you insert it into the wave equation they want me to find (look in problem 2a to see what I mean), which obviously can't be right.

But where is the fault in my derivation?

 

[Nikitin]

Ahh, but of course, the charge density is zero in an ideal conductor, is it not? Then what I get out will be nonsense because of that?