Question 1. Verify that y- 2y = r- + c is a family of implicit solutions of the differential equation (2y- 2)y = 20 -1 Find a member of the family satisfying y(0)= 1 Question 2. Find values of m so that e"ma is a solution of the differential equation y"-3y'+2y = 0 Question 3. Consider the autonomous differential equation y' = y(y - 7y+ 10) Find all equilibrium solutions. Sketch a phase portrait. For each equilibrium solution, determine whether the solution is stable, semi-stable, or unstable. Sketch several typical non-constant solution curves. Question 4. (The slope field question). Consider the differential equation y = r + 3. In what direction would you draw the slope field segment through the point (3,-1). Question 5. Suppose a population of rodents satisfies the differential equation dP dt Find a general solution of the differential equation. If there are initially 2 rodents, and after 1 months there are 10 rodents. figure out when there will be 1000 rodents. Explain why this model cannot be accurate over long time scales.

Question 1. Verify that y- 2y = r- + c is a family of implicit solutions of the differential equation (2y- 2)y = 20 -1 Find a member of the family satisfying y(0)= 1 Question 2. Find values of m so that e"ma is a solution of the differential equation y"-3y'+2y = 0 Question 3. Consider the autonomous differential equation y' = y(y - 7y+ 10) Find all equilibrium solutions. Sketch a phase portrait. For each equilibrium solution, determine whether the solution is stable, semi-stable, or unstable. Sketch several typical non-constant solution curves. Question 4. (The slope field question). Consider the differential equation y = r + 3. In what direction would you draw the slope field segment through the point (3,-1). Question 5. Suppose a population of rodents satisfies the differential equation dP dt Find a general solution of the differential equation. If there are initially 2 rodents, and after 1 months there are 10 rodents. figure out when there will be 1000 rodents. Explain why this model cannot be accurate over long time scales.

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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