# Math 230 - Chapters 1-3 Study Guide

1. State the order of the given ordinary differential equation and determine whether it is linear or non-linear. Look at problems 1.1.1-8.
2. Verify that the indicated family of functions is a solution of the differential equation. Look at problems 1.1.21-24.
3. Given the general solution and initial conditions to a differential equation, find the solution to the initial value problem. Look at problems 1.2.1-14.
4. Given the graph of the solution to a differential equation, determine which set of initial conditions was used. Look at problems 1.2.35-38. Multiple choice.
5. Given a direction field, sketch a solution curve that passes through the indicated point. Look at problems 2.1.1-4.
6. Given a graph of several solution curves to an autonomous differential equation, identify the critical points, create a phase portrait, and classify each critical point as an attractor, repeller, or semi-stable. Finally, write an equation that could have the solutions shown. Look at problems 2.1.21-28 and figure 2.6.
7. Solve the differential equation using separation of variables. Look at problems 2.2.1-22.
8. Solve the differential equation using the intergrating factor. Look at problems 2.3.31-24.
9. Verify that the differential equation is exact and then solve it. Look at problems 2.4.1-20.
10. The graph of a series circuit is shown. Setup and solve the differential equation. Look at problems 3.1.27 and 3.1.29 and example 6 in section 3.1. Be sure you know formulas 7 and 8 in section 3.1.
11. Solve the differential equation by making an appropriate substitution. Look at problems 2.5.1-10.
12. Solve the Bernoulli equation by making an appropriate substitution. Look at problems 2.5.15-20.
13. Solve the differential equation by making an appropriate substitution. Look at problems 2.5.23-28.
14. Write a differential equation to model the described situation. Do not solve the differential equations, only set them up. Two parts. Look at problems 1.3.1-15

## Take Home Exam

There is a take home exam for the problems in chapter 3. These problems are due the day of the in-class exam. Each problem is worth 5 points.

1. Problem 3.1.12
2. Problem 3.1.18
3. Problem 3.1.36
4. Problem 3.2.4
5. Problem 3.2.24
6. Problem 3.3.6

## Notes:

• You may have a note card with certain formulas on it. These cards may not have worked out examples. Here are the formulas you may have.
• For section 2.5, you may write out the substitution formulas and when they are appropriate. For example, for homogeneous equations, you might write something like "A first-order DE in differential form is said to be homogeneous if both functions M and N are homogeneous equations of the same degree. A homogeneous function means f(tx,ty) = tnf(x,y) for some power of n. For a homogeneous DE in this form, use the substitution y=ux or x=vy".
• For section 2.5, you should also write down the setup and subsitutions for Bernoulli equations and equations of the form dy/dx = f(Ax+By+C)
• You may write down the formulas for the voltage drops across an inductor, resistor, and capacitor as well as the relationship between current and charge.
• There is a take home exam worth 30 points. It is due the day of the in-class exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 3 3 3 3 4 6 6 6 6 6 6 6 6 6 70