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[QUOTE]Originally posted by Gaseous Anomaly: [QB] OK, the equation I posted was a tricky one, and when I did it in my head, I must have been in "The Zone", or something. No matter!! Krenim: You're probably going to get medievil on my ass with a temporal inversion, but what you did was incorrect. You cannot split up an equation like that (i.e. a non-homogeneous eqn.) the way you did. Reason is that you're looking for y, and you integrated it [yx->(yx^2)/2) as if it were a constant, which it is not. Here's the way I did it: dy/dx = y-x. Multiply across by exp(-x). Get: [exp(-x)]dy/dx -y[exp(-x)] = -x[exp(-x)] Now use the Product Rule (for differentiation) backwards on the Left Hand Side(LHS): d(y[exp(-x)])/dx = -x[exp(-x)] (OK so far?) or d(y[exp(-x)]) = (-x[exp(-x)])dx. Integrating both sides, we get y*exp(-x) on the LHS, and after Integrating by Parts x*exp(-x) + exp(-x) on the RHS. NOW, if you divide across by exp(-x), you will be left with y =x + 1, which if checked satisfies the original equation (d(x+1)/dx =1 y(=x+1)-x =1) That's the way I did it. It's a bit of a hard one alright. Sorry about that. [IMG]http://solareclipse.net/Forums/smile.gif[/IMG] [/QB][/QUOTE]
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