Lhe practice problems are not supposed to be representative of the length of the test-in particular, the practice problems are (much) longer than the test will be. Question 1. Verify that y- 2y = x² –...

Extracted text: Lhe practice problems are not supposed to be representative of the length of the test-in particular, the practice problems are (much) longer than the test will be. Question 1. Verify that y- 2y = x² – 1 + 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 em 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 = kP2 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 6. Find a general solution to the differential cquation