Answer question 1 pls 1 of 4dyUse GeoGebra to create a direction field for the differential equationdx1.- y. Then use GeoGebra todraw an approximate solution curve that passes through the indicated points. (This will have 4 different curveson one picture. No written work needed here, just submit your screenshot/graphics file.)(а) у(—6) — 0(b) y(0) := 1(c) y(0)= -4(d) y(8)= -42. (а)In the theory of learning, the rate at which a subject is memorized is assumed to be proportional tothe amount that is left to be memorized. Suppose M denotes the total amount of a subject to be memorizedand A(t) is the amount memorized in time t. Determine a differential equation for the amount A(t). (SETUP ONLY. DO NOT SOLVE.)(b)in time t. Determine a differential equation for the amount A(t) when forgetfulness is taken into account.(SET UP ONLY. DO NOT SOLVE.)Now assume that the rate at which material is forgotten is proportional to the amount memorized3.Find the critical points and phase portrait of the autonomous first-order differential equationdy= y? (y+ 4)(y – 2). Classify each critical point as an attractor (asymptotically stable), repeller (unstable), ordxsemi-stable.dy+ 2(t + 1)y² = 0, y(0) = – §.dt4.Solve the IVP5.The temperature of a cup of coffee obeys Newton's law of cooling. The initial temperature of the coffeeis 200°F and one minute later, it is 180°F. The ambient temperature of the room is 66°F.(a) If T(t) represents the temperature of the coffee at time t, write the initial value problem that represents thisscenario.

Given: 1. dydx=x2-y and the points y(-6)=0, y(0)=1, y(0)=-4 and y(8)=-4.

dy Use GeoGebra to create a direction field for the differential equation = x2 – y. Then use GeoGebra to dx draw an approximate solution curve that passes through the indicated points. (This will have 4 different curves on one picture. No written work needed here, just submit your screenshot/graphics file.) (а) у(-6) — 0 (b) y(0) = 1 (с) у(0) — —4 (d) y(8) = -4

dy Use GeoGebra to create a direction field for the differential equation = x2 – y. Then use GeoGebra to dx draw an approximate solution curve that passes through the indicated points. (This will have 4 different curves on one picture. No written work needed here, just submit your screenshot/graphics file.) (а) у(-6) — 0 (b) y(0) = 1 (с) у(0) — —4 (d) y(8) = -4

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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