Okay, first of all:
Adrin took a mathematical shortcut. Technically, he should have integrated both sides of the equation with respect to x.
The integral of dy/dx with respect to x is y + a constant
The integral of (5x+4) with respect to x is (5x^2)/2 + 4x + a different constant.
Therefore y = (5x^2)/2 + 4x + C, where C is yet another constant.
Adrin's only real mistake was forgetting to add the constant of integration. And mis-copying the original problem.
Give him a break for using informal notation and lacking integral signs.
Secondly, e^(i*pi) = -1 is a form of Euler's Identity, which is a special case of Euler's Formula, which tells us that e^(i*x) = cos(x) + i*sin(x)
Plug pi in for x and see what you get.
And JDE is incorrect about how e is defined. e is not a number specially constructed to give that wacky relationship as JDE would imply.
e is actually defined numerically as the sum from n=0 to n=infinity of 1/n!
e is also defined as the base of the natural logarithm (which, incidentally, is "natural" because the derivative of ln(x) with respect to x is 1/x)
Yes, ln (x) came before e^x.
While JDE's definition
may be correct (and I'm not sure it is) it's signficantly less useful than either of those definitions.
So AM is not both right and wrong. He's just right.
Incidentally, e^(i*pi) = -1 is actually pretty dull compared to this:
i^(-i) = (e^pi)^(1/2)
-White Knight <p>
Behold! Sig figs!</p>
Edited by: [url=http://pub30.ezboard.com/brpgww60462.showUserPublicProfile?gid=whiteknightdelta>White] at: 10/18/03 1:29 pm