Math 230 - Chapter 2 Study Guide

  1. Given the graph of the solution to a differential equation, determine which set of initial conditions was used. Multiple choice; circle all correct responses.
  2. Given a direction field, sketch a solution curve that passes through the indicated point. Three parts.
  3. Consider the autonomous differential equation. Identify the critical points, make a phase portrait, and identify whether each critical point is asymptotically stable, unstable, or semi-stable. Two parts.
  4. Identify each differential equation as Autonomous, Separable, Linear, Exact, Homogeneous, Bernoulli, or None of these. More than one may apply and you should identify all that do apply. Ten parts.
  5. Find the integrating factor needed to make the equation exact and then multiply the equation by that. Do NOT solve the equation.
  6. Use a linear substitution and then separate the variables. Do NOT solve the equation.
  7. Use a substitution for a homogeneous differential equation and then separate. Do NOT solve the equation.
  8. Use Euler's method to approximate a value.
  9. Solve the initial value problem using separation of variables.
  10. Solve the initial value problem using the integrating factor.
  11. Solve the exact differential equation.
  12. Solve the Bernoulli equation by making an appropriate substitution.


Points per problem

# 1 2 3 4 5 6 7 8 9 10 11 12 Total
Pts 4 6 6 30 6 6 6 6 8 8 8 8 102