B: Study the stability of critical points of ODEs: -2x²+x²+x-2=0 and draw the phase portrait.
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- SOLVE THE ODE y''+9y=xexp(3x) + 6If the parent function y = V is shifted 4 units to the left and 3 units down, the new %3D function would be: Oy = VT - 4- 3 O y = Væ +4 – 3 - O y = Væ+4+3 o y = Vx - 4+3Are functions f(x) = x² – 2, g(x) = x² + 2x – 1 and h(x) = 2x² + 6x + 1 linearly dependent? If yes, write f(x) as a linear combination of g(x) and h(x).
- 1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.Suppose that while driving a car, the driver suddenly sees an animal standing in the road. The driver's brain registers the information and sends a signal to the driver's foot to hit the brake. The car travels a distance D, in feet, during this time, where D is a function of the speed r, in miles per hour, of the car when the driver sees 13 the animal. That reaction distance is a linear function given by D(r) = 10+ 5. Complete parts a through c below. a) Find the slope of this line and interpret its meaning in this application. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The slope m is |. For each mile per hour faster that the car travels, it takes feet longer to stop. O B. The slope is not defined. For each mile per hour faster that the car travels, it takes 0 foot longer to stop.The Different Effects of Excitation and Inhibition in Neural Circuit (series #1)| Neural circuit consists of polysynaptic neural network, combination of excitatory and inhibitory neurons. This exercise helps to understand the effects of excitation and inhibition in the nervous system. Our body is dynamically active under physiology condition. As a result, there are basal levels of activity such as 70 beats/min of heart rate at resting condition. Either increased or decreased activities are relative to the baseline. The effects of excitation are easily understood---one neuron activates another neuron. However, when inhibition is introduced into circuits, analysis become more complicated. In fact, the numbers of inhibitory neurons in the circuit determine the final effect of the circuit, which can be excitation or inhibition, on the target organ or area. We assume all excitatory and inhibitory neurons are glutamate and GABA neurons, respectively, in this practice sheet. The glutamate and…
- solve xsinydx+(x2+1)cosydy=0A phase trajectory is shown for populations of birds H and insects W. Sketch the graphs of H and W as functions of time. Assume that H (0) = 100 and W (0) = 20, 000Decide if the following functions are linearly independent in the interval (-00, 00) f1(2) = 1+r, f2(x) = x, fa(x)=r? %3D
