1. Consider the di?erential equation y\'= mx ? y, where m > 0 is a constant. Sho

Question

1. Consider the di?erential equation y'= mx ? y, where m > 0 is a constant. Show that there is a linear solution to the equation, and that all solutions approach it. For what value of y(0) is the particular solution to the equation the linear one? Finally, suppose that m = 2: what initial condition results in y(3) = 4.01? In y(3) = 4.001? 2. Suppose that the fraction of a population that has heard a rumor is modeled by the logistic equation P'= kP(1 ?(P/L)), where t is measured in days. What is L? If we initially have P(0) = 0.1 (10% of the population has heard the rumor), and the fraction is increasing at a rate of 18% per day, what is k? Separate variables and solve for P to determine at what time 90% of the population will have heard the rumor. 3. Consider the autonomous di?erential equation y'= ?y^2 + ky ? 4, where k is a constant. Sketch qualitatively accurate solution curves for each of k = 5, k = 4 and k = 3. How does the number of equilibrium solutions change? Draw a bifurcation diagram for this problem. 4. Suppose that an object is started with a velocity v0 in a medium in which the frictional resistance to motion is proportional to the cube of the object

Explanation / Answer

Too long!!!!!!!

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.