16.(A) -∞⁰3(B) -1210-1Ń-30Shown above is a slope field for the differential equation d = y² (1 − y²). If y = f(x) is the solution to thedifferential equation with initial condition f(1) = 2, then lim f(x) isdxx →∞(C) 012 3(D) 1(E) CO

Answered: 16. 3 2 1 0 -1 -3 0 1 2 3 - Shown above…

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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The dollar valuation V(t) of Batcoin as a function of time t, measured in days, is governed by the differential equation: dV dt -0.04V² + 80V (a) For what initial valuations would Batcoin remain priced at the same level? (b) Sketch a direction field describing this situation. You may assume that the Batcoin valuation never dips below zero. (c) Would Batcoin ever become essentially worthless? Justify your answer. (d) If you purchased a single Batcoin at its market price of $2500 today, approximately how much would your investment be worth six months from now? Use graphical analysis and explain your answer. =
(b) We have a mysterious function f. Which of the following can possibly be the slope field of the differential equation dy = f(t+y)? Give a short justification. // 10000 (II) (IV)
Recall that cos(x) = cos(x-л) and consider the differential equation on the domain x Є [0,л], у Є [0,π]. d x(t) = = sin(x) (cos(x)+cos(y)) Then, d dt (t) = sin(y) (cos(x) — cos(y)) • sketch the 6 nullclines of the differential equation in this region, • determine any equilibria, ⚫ determine the linear stability of equilibria points using the Jacobian matrix.
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Suppose the constant function y(t) = 2 (for all t) is a solution to the differential equation dy/dt = f(t,y). (a) What does this tell you about the function f(t,y)(b) What does this tell you about the slope field? In other words, how much of the slope field can you sketch using this information?(c) What does this tell you about solutions with initial conditions y(0) ̸= 2?
14. The slope field for a differential equation =f(x,y) is given in the figure. Which of the following statements are true? #3 I. A solution curve that contains the point (0, 2) also contains the point (-2, 0). II. As y approaches 1, the rate of change of y approaches zero. III. All solution curves for the differential equation have the same slope for a given value of y (A) I only (B) II only (C) I and II only NO CALCULATOR 1/1134 111111111 \\\!!!!۱۱/۱۱ (D) II and III only (E) I, II, III

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16. 3 2 1 0 -1 -3 0 1 2 3 - Shown above is a slope field for the differential equation d = y² (1 − y²). If y = f(x) is the solution to the differential equation with initial condition f(1) = 2, then lim f(x) is dx