Chick Sniffy This differential equation y” + 4y’ + 4y has repeated roots and one solution might be y = 2xexp(-2x) + 2exp(-2x) Just to verify that y'(0) = -2, (see graph) y'(0) = -4xexp(-2x) + 2(exp(-2x) -4exp(-2x) = 0 + 2 – 4 = -2 If function y = Y(x), then a family ofContinue reading “Second Order Differential Equation and Aural Trajectories”
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The Origin of the Slime
Photosynthesis dramatically changed the planet and in turn, would not be possible without the nitrogen molecule-otherwise, the rest is simply hydrocarbons. Near the end the 18th century methods were coming online for the synthesis of ammonia (NH4). The starting materials are simple enough: Water, natural gas, and of course Nitrogen. But even now, the needContinue reading “The Origin of the Slime”
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