Second Order Differential Equation and Aural Trajectories

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”

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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