Consider the following system of differential equations à ý 2x - x² - y 1. The point (-2,-8), (0,0) and (1, 1) are equilibrium points for the system. Try to decide if they are locally asymptotically stable or saddle points. 2. Draw a phase diagram and indicate the above equilibrium points. For the quadrant * 20 and y ≥ 0 partition the phase diagram into regions with similar direction of motion. Indicate the direction of motion in each of the sectors by using arrows.

7. Sketch a phase portrait for the system x₁ = 4x₁ + 10x2, x2 = x1 - 5x2. You should sketch several typical solution curves in the x₁x2-plane.

Consider the non-linear differential equation * =- x + y - 1 ý = 2x + x3. Draw the nullclines and a qualitative phase portrait for the non-linear system. Indicate the stable and unstable manifold.

Just 4b please! Diff eq

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.50 – 0.01x and o = 0.07. n USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For an 8°F increase in temperature? 1°F increase -0.01 hr 8°F increase -0.08 hr (b) What is the expected reaction time when temperature is 220°F? When temperature is 260°F? 220°F 3.3 hr 260°F 2.9 hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.78 and 3.02 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal…

Classification. Determine whether the following differential equations are linear or nonlinear. Also, state the order and degree. 1. xy' – y = x2 2. 2хуу' + у? %3 -х? 3. (у")2 — 2(у')* + ху %3D 0 4. у" + 2y' — 8у %3Dх2 + сos(x)

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Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.10 − 0.01x and ? = 0.07. (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 12°F increase in temperature? 1°F increase      hr 12°F increase      hr (b) What is the expected reaction time when temperature is 190°F? When temperature is 240°F? 190°F      hr 240°F      hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 240°F. What is the probability that all five times are between 2.58 and 2.82 hours? (Round your answer to four decimal places.)(d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal…

Prealgebra Draw the phase lines of the following differential equations. List all the equilibrium points for each system, and classify them as stable or unstable. (1.1) dx/dt = square root5 - ex, (1.2) dx/dt = 32x+1 -28(3×)+9, (1.3) dx/dt = xlnx _x³ e².

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 4.10 - 0.01x and o = 0.07. n USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 9°F increase in temperature? 1°F increase hr g°F increase hr (b) What is the expected reaction time when temperature is 190°F? When temperature is 260°F? 190°F hr 260°F hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 1.39 and 1.61 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal places.)