Solve the following linear system and sketch its phase portrait * = [¹ =1] x.
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- Find the general solution and sketch the phase portrait of 1 z - ( -5₂5) z z' -2 3Consider a disease where immunity is lost. On average, aftern days, a recovered person becomes susceptible again. Adjust the equationsfor ds/dt , di/dt, and dr/dt in the SIR model to account for this.Differentiate y = cos³x³
- Scientists have studied the annual biorhythm of the excretion of norepinephrine (a hormone and a neurotransmitter) in a healthy human. The level varies from a low of 12 units to a high of 20 units and has a period of 12 months. Make a sine model of the level of norepinephrine if the initial level is 12 units. Use a phase shift of 3. (Express numbers in exact form. Use symbolic notation and fractions where needed. Let L = f(t) and give the equation in terms of L and t.) equation:Complete the table Equation y (5)_y(3) = e2+2x2²-5 y(4) + 5y" + 4y = sinx + cos2x Appropriate Form of the Particular SolutionSketch the phase portrait for( q3) only now in 30 min