Some Comments on the Exam

Q1 This is supposed to be the panic-breaker and is the problem that everyone should have gotten correct. If you had a hard time with this one, remember to slow down and do the easier problems carefully and correctly.

Q2 This is a separation of variables problem. Remember to add the constant right when you do the integral, not after you solve for y. Also remember that is if that was on your exam, and remember that in general

Q3 Remember that an equation is exact if and that x is an independent variable. Our constants cannot depend upon x.

Q4 Read the question carefully. It was not to solve the differential equation, but to find an integrating factor.

Q5 Read the question carefully. It was to write down the differential equation and solve it. If you remember the solution to this particular equation, good, but you still must answer the question and thus SOLVE the differential equation. Also, remember that the question asks "how long" so a reasonable answer would be some thing like "7 minutes from when the pizza came out of the oven." Also, review properties of logs if you made some errors working with them on this problem. Many people were zealous with non-existent log "simplifications."

Q6 Read the question. First solve the differential equation, and then show that any the difference of any two solutions satisfies the homogeneous differential equation. What are any two solutions? Something like and . You don't need to solve the homogeneous equation, just show that satisfies it.

Q7 State the method of solution if you are using a complicated one. This is a Bernoulli equation, so the word "Bernoulli" should appear in your solution. Also remember to substitute back so that your solution is for y, not u.

Q8 The differential equation for a family cannot involve any constants. So you need to eliminate c. You should be comfortable differentiating implicitly. You should be able to sketch hyperbolae- since we don't know if c is positive or negative, this family includes ones that open horizontally and vertically.

Q9 State the method of solution. If you do the subsititution , it is probably because is given by a homogeneous rational function of x and y, so the word "homogeneous" should appear in your work. You can also do this one as a Bernoulli, but it takes some care.

Q10 This was a tricky one but very similar to one on the sample exam. Very few people were able to set it up.

Upcoming Front Row Duty

By last name:
March 6: S-Z , March 11: N-R, March 13: morning class G-M, noon class I-M
March 18: morning class A-F, noon class A-H, March 20: S-Z , March 25:N-R
March 27:morning class G-M, noon class I-M, April 1: morning class A-F, noon class A-H, and then repeating if this works smoothly.